2 organizing and displaying data

Organizing and Displaying DataOrganizing and Displaying Data
Any survey or experiment yields a list ofAny survey or experiment yields a list of
observations. These need to be organized andobservations. These need to be organized and
summarized in a logical fashion so that we maysummarized in a logical fashion so that we may
perceive the outcome clearly.perceive the outcome clearly. TablesTables,, graphsgraphs
andand numericalnumerical methods are popularly used tomethods are popularly used to
organize and summarize data and description oforganize and summarize data and description of
data.data.

Education Weight Height Age Smoking Physical Blood Serum Syst. Bld Salary Ponderal
ID Sex level (Kg) (cm) status Activity Glucose Cholesterol Pressure $ index
1 M 2 70 165 61 1 1 107 199 102 $27,000 40.0361
2 M 1 60 162 52 0 2 145 267 138 $18,750 41.3807
3 F 1 62 150 52 1 1 237 272 190 $12,000 37.8990
4 F 2 66 165 51 1 1 91 166 122 $13,200 40.8291
5 M 2 70 162 51 0 1 185 239 128 $21,000 39.3081
6 M 4 59 165 53 0 2 106 189 112 $13,500 42.3838
7 M 1 47 160 61 0 1 177 238 128 $18,750 44.3357
8 F 3 66 170 48 1 1 120 223 116 $9,750 42.0663
9 F 4 56 155 54 0 2 116 279 134 $12,750 40.5137
10 F 2 62 167 48 0 1 105 190 104 $13,500 42.1942
11 F 4 68 165 49 1 2 109 240 116 $16,500 40.4248
12 M 1 65 166 48 0 1 186 209 152 $12,000 41.2861
13 M 1 56 157 55 0 2 257 210 134 $14,250 41.0365
14 F 2 80 161 49 0 1 218 171 132 $16,800 37.3648
15 M 3 66 160 50 0 2 164 255 130 $13,500 39.5918
16 M 4 91 170 52 0 2 158 232 118 $15,000 37.7951
17 M 3 71 170 48 1 1 117 147 136 $14,250 41.0547
18 M 5 66 152 59 0 2 130 268 108 $27,510 37.6122
19 M 1 73 159 59 0 2 132 231 108 $14,250 38.0443
20 F 4 59 161 52 0 1 138 199 128 $11,550 41.3563
21 F 1 64 162 52 1 1 131 255 118 $15,000 40.5000
22 M 3 55 167 52 1 1 88 199 134 $12,750 43.9132
23 F 2 78 175 50 1 1 161 228 178 $11,100 40.9581
24 F 2 59 160 54 0 1 145 240 134 $9,000 41.0994
25 F 3 51 167 48 1 2 128 184 162 $9,000 45.0325
26 M 3 83 171 55 0 1 231 192 162 $12,600 39.2016
27 M 2 66 157 49 1 2 78 211 120 $27,480 38.8495
28 M 4 61 165 51 0 1 113 201 98 $14,250 41.9154
29 M 2 65 160 53 0 1 134 203 144 $79,980 39.7938
30 M 3 75 172 49 0 1 104 243 118 $14,250 40.7857
31 M 4 61 164 49 0 2 122 181 118 $14,250 41.6614
32 M 1 73 157 53 1 2 442 382 138 $45,000 37.5657
33 M 2 66 157 52 0 1 237 186 134 $15,000 38.8495

Continued
34 M 1 73 155 48 0 2 148 198 108 $39,990 37.0872
35 M 2 61 160 53 0 1 231 165 96 $30,000 40.6453
36 F 3 68 162 50 0 2 161 219 142 $11,250 39.6898
37 M 2 52 157 50 0 2 119 196 122 $13,500 42.0628
38 M 5 73 162 50 0 1 185 239 146 $15,000 38.7621
39 M 1 52 165 61 1 2 118 259 126 $15,000 44.2062
40 F 1 56 162 53 1 1 98 162 176 $9,000 42.3434
41 F 3 67 170 48 1 2 218 178 104 $11,550 41.8560
42 M 1 61 160 47 0 1 147 246 112 $16,500 40.6453
43 M 3 52 166 62 1 2 176 176 140 $14,250 44.4741
44 M 2 61 172 56 1 2 106 157 102 $14,250 43.6937
45 M 3 62 164 55 1 2 109 179 142 $13,500 41.4362
46 F 2 56 155 57 1 2 138 231 146 $12,750 40.5137
47 F 1 55 157 50 0 2 84 183 92 $16,500 41.2837
48 M 3 66 165 48 1 2 137 213 112 $14,100 40.8291
49 M 1 59 159 51 0 2 139 230 152 $16,500 40.8426
50 M 3 53 152 53 1 2 97 134 116 $23,730 40.4655
51 M 5 71 173 52 0 2 169 181 118 $15,000 41.7792
52 M 2 57 152 49 0 1 160 234 128 $15,000 39.4959
53 M 2 73 165 50 1 1 123 161 116 $26,250 39.4799
54 M 3 75 170 49 0 2 130 289 134 $13,500 40.3115
55 M 3 80 171 50 1 2 198 186 108 $15,000 39.6856
56 M 4 49 157 53 0 1 215 298 134 $13,500 42.9043
57 M 4 65 162 52 0 1 177 211 124 $15,750 40.2912
58 F 2 82 170 56 0 2 100 189 124 $13,500 39.1301
59 M 3 55 155 52 0 2 91 164 114 $14,250 40.7578
60 M 3 61 165 58 0 1 141 219 154 $15,000 41.9154
61 M 2 50 155 45 1 2 139 287 114 $9,750 42.0735
62 M 5 58 160 56 0 1 176 179 114 $21,750 41.3343
63 M 1 55 166 50 1 2 218 216 98 $26,250 43.6503
64 M 5 59 161 47 0 2 146 224 128 $21,000 41.3563
65 M 2 68 165 53 1 1 128 212 130 $14,550 40.4248
66 M 2 60 170 53 1 2 127 230 122 $30,000 43.4242

Continued
67 M 1 77 160 47 1 1 76 231 112 $21,240 37.6088
68 M 5 60 155 52 0 1 126 185 106 $21,480 39.5927
69 M 3 70 164 54 0 1 184 180 128 $25,000 39.7934
70 M 2 70 165 46 0 1 58 205 128 $20,250 40.0361
71 M 2 77 160 58 1 1 95 219 116 $34,980 37.6088
72 F 5 86 160 53 0 2 144 286 154 $18,000 36.2483
73 F 2 67 152 49 1 2 124 261 126 $10,500 37.4242
74 F 3 77 165 53 1 1 167 221 140 $19,500 38.7841
75 F 3 75 169 57 0 2 150 194 122 $11,550 40.0743
76 F 2 70 165 52 0 2 156 248 154 $11,550 40.0361
77 F 2 70 165 49 1 1 193 216 140 $11,400 40.0361
78 F 1 71 157 53 0 1 194 195 120 $10,500 37.9152
79 F 1 55 162 49 0 2 73 217 140 $14,550 42.5985
80 F 2 59 165 53 1 2 98 186 114 $18,000 42.3838
81 F 3 64 159 50 0 2 127 218 122 $10,950 39.7500
82 F 1 66 160 54 0 1 153 173 94 $14,250 39.5918
83 F 4 59 165 60 0 2 161 221 122 $11,250 42.3838
84 F 3 68 165 57 0 1 194 206 172 $10,950 40.4248
85 M 5 58 160 52 0 1 87 215 100 $17,100 41.3343
86 M 1 57 154 65 1 1 188 176 150 $15,750 40.0156
87 M 2 60 160 65 0 2 149 240 154 $14,100 40.8698
88 M 2 53 162 62 0 1 215 234 170 $28,740 43.1277
89 M 2 61 159 62 1 2 163 190 140 $27,480 40.3912
90 F 1 66 154 62 0 1 111 204 144 $9,750 38.1071
91 F 1 61 152 67 0 2 198 256 156 $11,250 38.6130
92 F 2 52 152 66 0 2 265 296 132 $10,950 40.7233
93 F 1 59 155 62 0 2 143 223 140 $10,950 39.8151
94 F 1 63 155 62 1 1 136 225 150 $10,050 38.9540
95 F 2 61 165 63 0 2 298 217 130 $10,500 41.9154
96 M 2 68 155 67 0 2 173 251 118 $15,000 37.9748
97 M 1 58 170 62 0 1 148 187 162 $19,500 43.9177
98 M 3 68 160 55 0 1 110 290 128 $15,000 39.1998
99 F 5 60 159 50 0 2 188 238 130 $10,950 40.6144
100 M 2 61 160 54 1 1 208 218 208 $27,480 40.6453

The Frequency TableThe Frequency Table
Considerable information can be obtained from large massesConsiderable information can be obtained from large masses
of statistical data by grouping the data into classes andof statistical data by grouping the data into classes and
determining the number of observations that fall in each ofdetermining the number of observations that fall in each of
the classes. Such an arrangement is called athe classes. Such an arrangement is called a frequencyfrequency
distributiondistribution oror frequency tablefrequency table.. Frequency table may be theFrequency table may be the
most convenient way of summarizing or displaying data.most convenient way of summarizing or displaying data.
The types of frequency distributions that will be considered here are
categorical or qualitative frequency distributions, and grouped
frequency distributions.

Categorical or QualitativeCategorical or Qualitative
Frequency DistributionsFrequency Distributions
RRepresent data that can be placed in specific categories, suchepresent data that can be placed in specific categories, such
as gender, hair color, oras gender, hair color, or blood group.blood group.
ExampleExample:: The blood types of 25 blood donors are givenThe blood types of 25 blood donors are given
below. Summarize the data using a frequency distribution.below. Summarize the data using a frequency distribution.
AB B A O B
O B O A O
B O B B B
A O AB AB O
A B AB O A

SolutionSolution
AB B A O B
O B O A O
B O B B B
A O AB AB O
A B AB O A
Class (Blood Type) Frequency
A 5
B 8
O 8
AB 4
Total 25

Grouped Frequency DistributionGrouped Frequency Distribution
A grouped frequency distribution is obtained by constructingA grouped frequency distribution is obtained by constructing
class intervals for the data, and then listing the correspondingclass intervals for the data, and then listing the corresponding
number of values (frequency count) in each interval.number of values (frequency count) in each interval.
Class Interval
(Systolic Blood Pressure*) Tally
f
(Frequency)
90-109 10
110-129 24
130-149 18
150- 169 9
170-189 2
190-209 0
Total n =63
Frequency Table for Systolic Blood Pressure of Nonsmokers

How to construct a frequency table?How to construct a frequency table?
1. Arrange the data into an1. Arrange the data into an
array, a listing of allarray, a listing of all
observations fromobservations from
smallest to largest insmallest to largest in
order to determine theorder to determine the
interval spanned by theinterval spanned by the
data. We find that thedata. We find that the
overall blood pressureoverall blood pressure
interval is 92-172.interval is 92-172.
Systolic Blood Pressure of Non-Smokers
92 112 122 128 134 144 162
94 112 122 128 134 146 170
96 114 122 128 134 152 172
98 114 122 128 134 152
100 118 124 130 134 154
104 118 124 130 138 154
106 118 128 130 140 154
108 118 128 132 140 154
108 118 128 132 142 156
108 120 128 134 144 162

2.2. Determine theDetermine the rangerange
from the differencefrom the difference
between the smallestbetween the smallest
and largest value in theand largest value in the
set of observations i.e.set of observations i.e.
RR = 172-92 =80 mm= 172-92 =80 mm..
3.3. Divide the range into aDivide the range into a
number of equal andnumber of equal and
nonoverlappingnonoverlapping
segments calledsegments called classclass
intervalsintervals..
Systolic Blood Pressure of Non-
Smokers
92 112 122 128 134 144 162
94 112 122 128 134 146 170
96 114 122 128 134 152 172
98 114 122 128 134 152
100 118 124 130 134 154
104 118 124 130 138 154
106 118 128 130 140 154
108 118 128 132 140 154
108 118 128 132 142 156
108 120 128 134 144 162

The number of intervalsThe number of intervals
in general should rangein general should range
fromfrom 5 to 155 to 15..
WithWith too manytoo many classclass
intervals, the data areintervals, the data are
not summarizednot summarized
enough for a clearenough for a clear
visualization of howvisualization of how
they are distributed.they are distributed.
Class Interval
f
(Frequency)
90-94 0
95-99 2
100-104 3
105-109 | 1
110-114 4
115-119 4
120-124 | 6
125-129 | 6
130-134 | 11
135-139 8
140-144 3
145-149 3
150-154 | 1
155-159 | 6
160-164 | 1
165-169 2
170-174 | 1
175179 | 1
180-184 0
Total n =63
NoteNote

Class Interval
f
(Frequency)
90-149 52
150- 209 | 11
Total n =63
WithWith too fewtoo few, the data are, the data are oversummarizedoversummarized and some of the details of theand some of the details of the
distribution may lost.distribution may lost.
NoteNote

In order to determine the number of class intervals, useIn order to determine the number of class intervals, use Sturges’sSturges’s
formula;formula;
k = 1 + 3.322(log10 n)k = 1 + 3.322(log10 n),,
wherewhere kk stands for the number of class intervals andstands for the number of class intervals and nn is theis the
number of values in the data set under consideration (or thenumber of values in the data set under consideration (or the
sample size)sample size)
Example:Example: Suppose that we have a sample of 63 observations thatSuppose that we have a sample of 63 observations that
we want to group.we want to group.
kk = 1 + 3.322(log= 1 + 3.322(log1010 63)63) where 63 is the number of non-smokerwhere 63 is the number of non-smoker
in our examplein our example
kk = 1 + 3.322(1.8) = 5.98 6= 1 + 3.322(1.8) = 5.98 6
The answer obtained by Sturges’ rule should not considered asThe answer obtained by Sturges’ rule should not considered as
final,final, but as guide onlybut as guide only, should be increased or decreased for, should be increased or decreased for
convenience and clear presentation.convenience and clear presentation.
In practice, other consideration might cause us to use 8 orIn practice, other consideration might cause us to use 8 or
perhaps 10 or more class intervals. Suppose we decide that weperhaps 10 or more class intervals. Suppose we decide that we
want 6 intervals.want 6 intervals.
3. Class intervals3. Class intervals
~~
==

4.4. Determine the size (length or width)Determine the size (length or width) of the class interval (of the class interval (ww) by) by
dividing the range (dividing the range (RR) by the number of class intervals required or) by the number of class intervals required or
((kk), i.e.), i.e.
w ≥ R/kw ≥ R/k = 80/6 = 13.33= 80/6 = 13.33
The answer obtained could be increased or decreased forThe answer obtained could be increased or decreased for
convenience and clear presentation.convenience and clear presentation.
 It could be 15It could be 15
 However, for easiness and for comparison purposes we willHowever, for easiness and for comparison purposes we will
use 20use 20

5.5. Construct a table with three columns, andConstruct a table with three columns, and
then write the class intervals in the first column.then write the class intervals in the first column.
 Start the first class interval with the smallestStart the first class interval with the smallest
value or less. This value is called as thevalue or less. This value is called as the lowerlower
class limitclass limit..
ExampleExample:: The smallest value for systolic bloodThe smallest value for systolic blood
pressure of smokers is 92. For easiness, we willpressure of smokers is 92. For easiness, we will
begin at 90.begin at 90.

Class interval
(Systolic Blood Pressure*)
90
110
•Add the class width to this number to get the lower classAdd the class width to this number to get the lower class
limit of the next class interval.limit of the next class interval.

Class interval
90
110
•Determine the first class interval which contains all the values between
the lower class limits of two successive intervals including the lower
class limit of the first class interval.
i.e., 90, 91, 92, 93, 94, ……………………………. 109
The 109 here is called the upper class limits.
-109-109

Class interval
90
110
-109-109
-129
130 -149
150 -169
170 -189
190 -209
d. Repeat the above steps for the second, third, …….until thed. Repeat the above steps for the second, third, …….until the
last class intervallast class interval

Class interval
Total
90
110
-109-109
-129
130 -149
150 -169
170 -189
190 -209
Intervals are usually equal in size (= 20), thereby aiding the comparisonsIntervals are usually equal in size (= 20), thereby aiding the comparisons
between the frequencies of any intervals.between the frequencies of any intervals.
The upper limit of the last interval consists of either the largest value orThe upper limit of the last interval consists of either the largest value or
larger.larger.

Class interval
Total
90
110
-109-109
-129
130 -149
150 -169
170 -189
190 -209
6. Insert in the next column provided a tally for each individual6. Insert in the next column provided a tally for each individual
observation in the raw data table.observation in the raw data table.
Note that, the tally column is included simply as an aid for determiningNote that, the tally column is included simply as an aid for determining
the frequencies. It is not a necessary part of a frequency table.the frequencies. It is not a necessary part of a frequency table.

Class IntervalClass Interval
(Systolic Blood(Systolic Blood
Pressure*)Pressure*)
TallyTally
TotalTotal
162144134128120108
156142132128118108
154140132128118108
154140130128118106
154138130124118104
154134130124118100
15213412812211498
17215213412812211496
17014613412812211294
16214413412812211292
162144134128120108
156142132128118108
154140132128118108
154140130128118106
154138130124118104
154134130124118100
15213412812211498
17215213412812211496
17014613412812211294
1621441341281221129290 -109-109
110 -129
130 -149
150 -169
170 -189
190 -209
6. Insert in the next column provided a tally for each individual6. Insert in the next column provided a tally for each individual
observation in the raw data table.observation in the raw data table.
Note that, the tally column is included simply as an aid forNote that, the tally column is included simply as an aid for
determining the frequencies. It is not a necessary part of a frequencydetermining the frequencies. It is not a necessary part of a frequency
table.table.
||||
|||| |||| |||| |||| ||||
|||| |||| |||| |||
|||| ||||
||
||||

TallyTally
ff
(Frequency)(Frequency)
1010
2424
1818
99
22
00
TotalTotal
90 -109-109
110 -129
130 -149
150 -169
170 -189
190 -209
8.8. Sum the tally in each row and record them in the third columnSum the tally in each row and record them in the third column
entitledentitled FrequencyFrequency ((ff).).
|||| ||||
|||| |||| |||| |||| ||||
|||| |||| |||| |||
|||| ||||
||

TallyTally
ff
1010
2424
1818
99
22
00
TotalTotal nn = 63= 63
90 -109-109
110 -129
130 -149
150 -169
170 -189
190 -209
9. Sum the frequency column (9. Sum the frequency column (nn). This serves as a useful check). This serves as a useful check
that all data have been included in the table.that all data have been included in the table.
|||| ||||
|||| |||| |||| |||| ||||
|||| |||| |||| |||
|||| ||||
||

TallyTally
ff
1010
2424
1818
99
22
00
90 -109-109
110 -129
130 -149
150 -169
170 -189
190 -209
Note:Note:
Frequency tables should be numbered, includes an appropriate descriptiveFrequency tables should be numbered, includes an appropriate descriptive
titletitle, specify the, specify the units of measurementunits of measurement,, and cite theand cite the source of datasource of data..
|||| ||||
|||| |||| |||| |||| ||||
|||| |||| |||| |||
|||| ||||
||
Table 3.2 Frequency Table for Systolic Blood Pressure of Nonsmokers from TableTable 3.2 Frequency Table for Systolic Blood Pressure of Nonsmokers from Table
3.13.1
*In millimeters of mercury

Frequency Tables withFrequency Tables with class boundariesclass boundaries
Class boundaries may be used instead of class limits.Class boundaries may be used instead of class limits. ClassClass
boundariesboundaries are points that demarcate the true upper limit of oneare points that demarcate the true upper limit of one
class and the true lower limit of the next. Class boundaries can beclass and the true lower limit of the next. Class boundaries can be
easily obtained byeasily obtained by subtractingsubtracting from the lower limit andfrom the lower limit and addingadding to theto the
upper limitupper limit one-half of the smallest unit usedone-half of the smallest unit used to record the data.to record the data.
ExampleExample
Determine the class boundaries for the class intervalDetermine the class boundaries for the class interval 3.425-3.4293.425-3.429
For this interval, the smallest unit is 0.001. Thus, 0.001/2 is 0.0005 andFor this interval, the smallest unit is 0.001. Thus, 0.001/2 is 0.0005 and
so we get the class boundaries of the class interval asso we get the class boundaries of the class interval as
3.425 – 0.0005 = 3.42453.425 – 0.0005 = 3.4245
3.429 + 0.0005 = 3.42953.429 + 0.0005 = 3.4295
Thus the class boundaries will beThus the class boundaries will be 3.4245-3.42953.4245-3.4295, where the number, where the number
3.4245 is called the3.4245 is called the lower class boundarylower class boundary and 3.4295 is called theand 3.4295 is called the
upper class boundaryupper class boundary..

Frequency Tables withFrequency Tables with class boundariesclass boundaries
ForFor ourour example, the smallest unit is 1. Thus we use 0.5, so we getexample, the smallest unit is 1. Thus we use 0.5, so we get
the class boundaries of the first true class interval asthe class boundaries of the first true class interval as
90 minus 0.5 = 89.590 minus 0.5 = 89.5
and 109 plus 0.5 = 109.5and 109 plus 0.5 = 109.5
i.e., 89.5-109.5i.e., 89.5-109.5
(Upper limit of one class + lower limit of next class)(Upper limit of one class + lower limit of next class)
divided by twodivided by two
Alternative way for calculating Class BoundariesAlternative way for calculating Class Boundaries

Class boundaryClass boundary
ff
89.5-109.5 1010
109.5-129.5109.5-129.5 2424
129.5-149.5129.5-149.5 1818
149.5-169.5149.5-169.5 99
169.5-189.5169.5-189.5 22
189.5-209.5189.5-209.5 00
90 -109-109
110 -129
130 -149
150 -169
170 -189
190 -209
*In millimeters of mercury
ForFor ourour example, the smallest unit is 1. Thus we use 0.5, so we getexample, the smallest unit is 1. Thus we use 0.5, so we get
the class boundaries of the first true class interval asthe class boundaries of the first true class interval as
90 minus 0.5 = 89.590 minus 0.5 = 89.5
and 109 plus 0.5 = 109.5and 109 plus 0.5 = 109.5
i.e., 89.5-109.5i.e., 89.5-109.5

Relative frequencyRelative frequency
The relative frequency for a particular class is found byThe relative frequency for a particular class is found by
dividingdividing the class frequency by the total of all frequenciesthe class frequency by the total of all frequencies
(sample size) i.e.,(sample size) i.e., f/nf/n..
ExampleExample, the relative frequency of the first class, 90-109 mm of, the relative frequency of the first class, 90-109 mm of
nonsmoker isnonsmoker is
10/63= 0.1610/63= 0.16
If each relative frequency is multiplied by 100%, we have aIf each relative frequency is multiplied by 100%, we have a
percentage relative frequencypercentage relative frequency ((pp),),
i.e.i.e. p=(f/n).100p=(f/n).100..

For example, the relative frequency of the first class, 90-109 mmFor example, the relative frequency of the first class, 90-109 mm
of nonsmoker is (10/63)100 = 16%.of nonsmoker is (10/63)100 = 16%.
Class Interval
(Systolic Blood
Pressure*)
frequency Relative
Frequency (%)
Relative
frequency
90-109 10 16 0.16
110-129 24 38 0.38
130-149 18 29 0.29
150-169 9 14 0.14
170-189 2 3 0.03
190-209
Total
0
63
0
100
0
Frequency Table for systolic blood pressure of Nonsmokers
1

Class Interval
(Systolic Blood
Pressure*)
frequency Relative
Frequency (%)
90-109 5 14
110-129 15 41
130-149 10 27
150-169 3 8
170-189 2 5
190-209 2 5
Frequency Table for systolic blood pressure of Smokers
100

SignificanceSignificance
Class Interval
(Systolic Blood
Pressure*)
Relative Frequency
(%)
Nonsmokers Smokers
90-109 16 14
110-129 38 41
130-149 29 27
150-169 14 8
170-189 3 5
Helpful in makingHelpful in making comparisoncomparison between two sets of data that havebetween two sets of data that have
aa differentdifferent number of observations, like our 63 nonsmokers andnumber of observations, like our 63 nonsmokers and
37 smokers. For example, in the blood pressure range of 90-10937 smokers. For example, in the blood pressure range of 90-109
mm, 10 (16%) of the nonsmokers and 5 (14%) of the smokers weremm, 10 (16%) of the nonsmokers and 5 (14%) of the smokers were
represented.represented.

Cumulative relative frequency (cumulative percentage)Cumulative relative frequency (cumulative percentage)
Class Interval
(Systolic Blood
Pressure*)
Relative Frequency
(%)
Cumulative Relative Frequency
(%)
Nonsmokers Smokers Nonsmokers Smokers
90-109 16 14 16 14
110-129 38 41 54 55
130-149 29 27 83 82
150-169 14 8 97 90
170-189 3 5 100 95
It shows the percentage of elementsIt shows the percentage of elements lying within and below each classlying within and below each class
intervalinterval
Cumulative percentage can beCumulative percentage can be computedcomputed by cumulating the percentageby cumulating the percentage
relative frequencies of each of the various class intervals.relative frequencies of each of the various class intervals.

Cumulative relative frequency (cumulative percentage)Cumulative relative frequency (cumulative percentage)
Class Interval
(Systolic Blood
Pressure*)
Relative Frequency
(%)
(%)
Nonsmokers Smokers Nonsmokers Smokers
90-109 16 14 16 14
110-129 38 41 54 55
130-149 29 27 83 82
150-169 14 8 97 90
170-189 3 5 100 95
Make a rapidMake a rapid comparisoncomparison of entire frequency distributions, ruling out any needof entire frequency distributions, ruling out any need
to compare individual class intervals. For example, the 97%to compare individual class intervals. For example, the 97% ofof the nonsmokersthe nonsmokers
have a systolic blood pressurehave a systolic blood pressure belowbelow 169.5169.5. By comparison, 90% of the. By comparison, 90% of the
smokers have a blood pressuresmokers have a blood pressure below the same levelbelow the same level..
An alternate way of looking at this is to note thatAn alternate way of looking at this is to note that 3%3% of the nonsmokers andof the nonsmokers and
10%10% of the smokers have aof the smokers have a systolic blood pressure above 169.5.systolic blood pressure above 169.5.

Graphing Representation ofGraphing Representation of
DataData

Graphing Representation of DataGraphing Representation of Data
The information provided by a frequency distribution in tabularThe information provided by a frequency distribution in tabular
form is easier to grasp if presented graphically.form is easier to grasp if presented graphically.
Most people find a visual picture beneficial in comprehendingMost people find a visual picture beneficial in comprehending
the essential features of a frequency distribution.the essential features of a frequency distribution.
Despite the easiness of such visual aids to read than tables,Despite the easiness of such visual aids to read than tables,
they often do not give the same detail.they often do not give the same detail.

It is essential that each graph beIt is essential that each graph be self-explanatoryself-explanatory-- that is,that is,
havehave
 A descriptive title,A descriptive title,
 Labeled axes,Labeled axes,
 AnAn indication of the units of observation.indication of the units of observation.
 An effective graph should not attempt to present so muchAn effective graph should not attempt to present so much
information that it is difficult to comprehend.information that it is difficult to comprehend.
Graphing Representation of DataGraphing Representation of Data

HistogramsHistograms
AA histogram is a graphical display of a frequency distribution thathistogram is a graphical display of a frequency distribution that
uses classes and vertical bars (rectangles) of various heightsuses classes and vertical bars (rectangles) of various heights
to represent the frequencies. Histograms are useful when theto represent the frequencies. Histograms are useful when the
data values aredata values are quantitativequantitative..
A histogram gives anA histogram gives an estimate of the shape of the distributionestimate of the shape of the distribution ofof
the population from which one sample was taken.the population from which one sample was taken.

Class interval
(Systolic Blood
Pressure*)
Class
boundaries
f
(frequency)
90-109 89.5-109.5 5
110-129 109.5-129.5 15
130-149 129.5-149.5 10
150-169 149.5-169.5 3
170-189 169.5-189.5 2
190-209 189.5-209.5 2
Total n = 37
To make a histogramTo make a histogram
Make frequency table that shows class intervals and classMake frequency table that shows class intervals and class
frequencies.frequencies.
Determine theDetermine the classclass boundariesboundaries for each class interval.for each class interval.

Draw both abscissa (X or horizontal axis), which depicts theDraw both abscissa (X or horizontal axis), which depicts the classclass
boundariesboundaries (not limits), and a perpendicular(not limits), and a perpendicular ordinateordinate (Y or(Y or
vertical axis), which depicts thevertical axis), which depicts the frequencyfrequency (or relative frequency)(or relative frequency)
of observations.of observations.
Begin the vertical scaleBegin the vertical scale at zeroat zero..
Systolic blood pressure (mm Hg) for Non-Smoker
5
10
15
20
25
30
Frequency
0
89.5 109.5 129.5 149.5 169.5 209.5189.5
Note thatNote that, the height of the, the height of the
vertical scale shouldvertical scale should
equal to approximatelyequal to approximately
three-fourthsthree-fourths thethe
length of the horizontallength of the horizontal
scale. Otherwise, thescale. Otherwise, the
histogram may appearhistogram may appear
to be out of proportionto be out of proportion
with reality.with reality.

Once the scales have been laid out, a vertical bar is constructed aboveOnce the scales have been laid out, a vertical bar is constructed above
each class interval equal in height to itseach class interval equal in height to its class frequencyclass frequency..
When the size of class intervals is equal,When the size of class intervals is equal, frequencies are representedfrequencies are represented
by both the heightby both the height andand the area of each bar.the area of each bar. The total areaThe total area
represents 100%.represents 100%.
5
10
15
20
25
Frequency
For example: 16% of theFor example: 16% of the
area corresponds to thearea corresponds to the
10 scores in the class10 scores in the class
interval 89.5-109.5 andinterval 89.5-109.5 and
that 38% of the areathat 38% of the area
corresponds to the 24corresponds to the 24
observations in theobservations in the
second bar.second bar.
0
89.5 109.5 129.5 149.5 169.5 209.5189.5

A histogram gives the impression that frequencies jump suddenly fromA histogram gives the impression that frequencies jump suddenly from
one class to the next. If you want to emphasize the continuous rise orone class to the next. If you want to emphasize the continuous rise or
fall of the frequencies, you can use a frequency polygon or line graph.fall of the frequencies, you can use a frequency polygon or line graph.
Frequency PolygonFrequency Polygon
5
10
15
20
25
Frequency
Frequency Histogram
0
89.5 109.5 129.5 149.5 169.5 209.5189.5

A histogram gives the impression that frequencies jump suddenly fromA histogram gives the impression that frequencies jump suddenly from
one class to the next. If you want to emphasize the continuous rise orone class to the next. If you want to emphasize the continuous rise or
fall of the frequencies, you can use a frequency polygon or line graph.fall of the frequencies, you can use a frequency polygon or line graph.
5
10
15
20
25
Frequency
Frequency Polygon
0
89.5 109.5 129.5 149.5 169.5 209.5189.5

Frequency polygon uses the same axes as the histogram.Frequency polygon uses the same axes as the histogram.
5
10
15
20
25
Frequency
Frequency Polygon
0
89.5 109.5 129.5 149.5 169.5 209.5189.5

It is constructed by making a dot over theIt is constructed by making a dot over the class midpointclass midpoint at the heightat the height
of the class frequency. The coordinates of these dots are (classof the class frequency. The coordinates of these dots are (class
midpointmidpoint, class frequency). These points are then, class frequency). These points are then connectedconnected withwith
straight lines.straight lines.
0
5
10
15
20
25
30
89.5 109.5 129.5 149.5 169.5 189.5 209.5
Frequency
79.5 99.5 119.5 139.5 159.5 179.5 199.5midpoints
Computing Class Midpoints =Computing Class Midpoints =
lower class limit + upper class limitlower class limit + upper class limit
22

Note thatNote that the polygon is brought down to the horizontal axis at thethe polygon is brought down to the horizontal axis at the
ends at points that would be the midpoints if there were an additionalends at points that would be the midpoints if there were an additional
cell at each end of the corresponding histogram.cell at each end of the corresponding histogram.
0
5
10
15
20
25
30
Frequency
79.5 99.5 119.5 139.5 159.5 179.5 199.5

Frequency polygons areFrequency polygons are superiorsuperior, to histograms in, to histograms in
providing aproviding a means of comparingmeans of comparing two frequencytwo frequency
distributions.distributions.
In frequency polygons, theIn frequency polygons, the frequencyfrequency of observations inof observations in
a given class interval is represented by thea given class interval is represented by the areaarea
contained beneath the line segmentcontained beneath the line segment and within theand within the
class interval. This area is proportional to the totalclass interval. This area is proportional to the total
number of observations in the frequency distribution.number of observations in the frequency distribution.
Frequency polygons should be used to graphFrequency polygons should be used to graph onlyonly
quantitativequantitative (numerical) data, never qualitative (i.e.,(numerical) data, never qualitative (i.e.,
nominal or ordinal) data since these latter data are notnominal or ordinal) data since these latter data are not
continuous.continuous.

Frequency polygons may take on a number ofFrequency polygons may take on a number of differentdifferent
shapesshapes
"bell-shaped" symmetrical distribution."bell-shaped" symmetrical distribution.

shapesshapes
Bi-modal (having two peaks) distribution.Bi-modal (having two peaks) distribution.

shapesshapes
Rectangular distribution in which each classRectangular distribution in which each class
interval is equally represented.interval is equally represented.

shapesshapes
Asymmetrical positively (right) skewed distribution,Asymmetrical positively (right) skewed distribution,
since it tapers off in the positive direction.since it tapers off in the positive direction.

shapesshapes
Asymmetrical negatively (left) skewed. Both polygons areAsymmetrical negatively (left) skewed. Both polygons are
identified by the location of theidentified by the location of the tailtail of the curve (not by theof the curve (not by the
location of the hump – a common error).location of the hump – a common error).

Cumulative Frequency Polygons (Ogive)Cumulative Frequency Polygons (Ogive)
Ogive can be used toOgive can be used to
determine how manydetermine how many
scores are above orscores are above or
below a set level.below a set level.
0
.20
40
60
80
100
89.5 109.5 129.5 149.5 169.5 189.5 209.5
Systolic blood pressure
Cumulativerelativefrequency
90
50
0
20
40
60
80
89.5 109.5 149.5
Nonsmoker
Smoker
90
50

Class Interval
(Systolic Blood
Pressure*)
(%)
Nonsmokers Smokers
89.5-109.5 16 14
109.5-129.5 54 55
129.5-149.5 83 82
149.5-169.5 97 90
169.5-189.5 100 95
To make an ogiveTo make an ogive
 Make a frequency table showing class boundaries andMake a frequency table showing class boundaries and
cumulative frequencies.cumulative frequencies.

To make an ogiveTo make an ogive
 Use the same horizontal scale as that for a histogram,Use the same horizontal scale as that for a histogram,
whereas the vertical scale indicates cumulative frequency orwhereas the vertical scale indicates cumulative frequency or
cumulative relative frequency.cumulative relative frequency.
0
20
40
60
80
100
0
89.5 109.5 129.5 149.5 169.5 189.5 209.5
Systolic blood pressure (mmHg)

For each class interval, make a dot over theFor each class interval, make a dot over the upper classupper class
boundaryboundary at the height of the cumulative classat the height of the cumulative class
frequency. The coordinates of the dots are (upper classfrequency. The coordinates of the dots are (upper class
boundary, cumulative class frequency). Connect theseboundary, cumulative class frequency). Connect these
dots with line segments.dots with line segments.
0
20
40
60
80
100
89.5 109.5 129.5 149.5 169.5 189.5 209.5

By convention, an ogive begins on the horizontalBy convention, an ogive begins on the horizontal
axis at the lower class boundary of the first classaxis at the lower class boundary of the first class
interval.interval.
0
20
40
60
80
100
89.5 109.5 129.5 149.5 169.5 189.5 209.5

Ogive are useful in comparing two sets of data, as, for example,Ogive are useful in comparing two sets of data, as, for example,
data on healthy and diseased individuals.data on healthy and diseased individuals.
In The Figure below we can see that 90% of the nonsmokers andIn The Figure below we can see that 90% of the nonsmokers and
86% of the smokers86% of the smokers had systolic blood pressures below 160had systolic blood pressures below 160
mmHg.mmHg.
0
.20
40
60
80
100
89.5 109.5 129.5 149.5 169.5 189.5 209.5
Systolic blood pressure
90
50
0
20
40
60
80
89.5 109.5 149.5
Nonsmoker
Smoker
90
50

Class Interval
(Systolic Blood
Pressure*)
frequency Relative
Frequency
(%)
90-109 5 14
110-129 15 41
130-149 10 27
150-169 3 8
170-189 2 5
190-209 2 5Systolic blood pressure (mm Hg) for Non-Smoker
5
10
15
20
25
Frequency
0
89.5 109.5129.5149.5 169.5 209.5189.5
Stem-and-leaf DisplaysStem-and-leaf Displays
Frequency distributions and histograms provide a usefulFrequency distributions and histograms provide a useful
organization and summary of data. However, in aorganization and summary of data. However, in a
histogram, we lose most of the specific data values.histogram, we lose most of the specific data values. AA
stem-and-leaf displaystem-and-leaf display is a device that organizes andis a device that organizes and
groups data but allows us to recover the original data ifgroups data but allows us to recover the original data if
desired.desired.

Steps to follow in constructing a Stem and Leaf DisplaySteps to follow in constructing a Stem and Leaf Display
1.1. Divide each observation in the data set into two parts, the leftmostDivide each observation in the data set into two parts, the leftmost
part is called the Stem and the rightmost part is called the Leaf.part is called the Stem and the rightmost part is called the Leaf.
Stem
(Intervals)
Leaves
(Observation)
90-99 2
stem Leaf

 Stem consists of the first few digits of the values, but the leavesStem consists of the first few digits of the values, but the leaves
contains only the final digit of each value.contains only the final digit of each value. For grouped data, theFor grouped data, the
stem represents the class intervals while the leaves are the strings ofstem represents the class intervals while the leaves are the strings of
values within each class interval.values within each class interval.
Stem
(Intervals)
90-99
100-109
.
.
.
Stem
0.1
0.2
0.3
.
.
Stem
30
40
50
.
100
Stem
100
200
300
.
1000

Stem
(Intervals)
Leaves
(Observation)
90-99
1.1. List the stems in order from smallest to largest in a verticalList the stems in order from smallest to largest in a vertical
column. Draw a vertical line to the right of the stems.column. Draw a vertical line to the right of the stems.
110-119
120-129
130-139
140-149
150-159
160-169
170-179
180-189

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109
110-119
120-129
130-139 8
140-149
150-159
160-169
170-179
180-189
1.1. Place all the leaves with the same stem on the same row asPlace all the leaves with the same stem on the same row as
the stem, and arrange the leaves in increasing order. Proceedthe stem, and arrange the leaves in increasing order. Proceed
through the data set, placing the leaf for each observation inthrough the data set, placing the leaf for each observation in
the appropriate stem row.the appropriate stem row.
First data value = 138

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109
110-119
120-129 8
130-139 8
140-149
150-159
160-169
170-179
180-189
Second data value = 128

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109
110-119 2
120-129 8
130-139 8
140-149
150-159
160-169
170-179
180-189
Third data value = 112

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109
110-119 2
120-129 8 8
130-139 8
140-149
150-159
160-169
170-179
180-189
Next data value = 128

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109
110-119 2
120-129 8 8
130-139 8 4
140-149
150-159
160-169
170-179
180-189

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109 4
110-119 2
120-129 8 8
130-139 8 4
140-149
150-159
160-169
170-179
180-189

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109 4
110-119 2
120-129 8 8
130-139 8 4
140-149
150-159 2
160-169
170-179
180-189

Stem
(Intervals)
Leaves
(Observation)
90-99
100-109 4
110-119 2
120-129 8 8
130-139 8 4 4
140-149
150-159 2
160-169
170-179
180-189

Proceed throughProceed through
the datathe data
setset

Stem
(Intervals)
Leaves
(Observation)
90-99 2 4 6 8
100-109 0 4 6 8 8 8
110-119 2 2 4 4 8 8 8 8 8
120-129 0 2 2 2 2 4 4 8 8 8 8 8 8 8 8
130-139 0 0 0 2 2 4 4 4 4 4 4 8
140-149 0 0 2 4 4 6
150-159 2 2 4 4 4 4 6
160-169 2 2
170-179 0 2
180-189
Arrange the leaves in increasing order.Arrange the leaves in increasing order.

NoteNote
The leaves portray a histogram laid on its side; each leaf reflects theThe leaves portray a histogram laid on its side; each leaf reflects the
values of thevalues of the observations, from which it is easy to note their sizeobservations, from which it is easy to note their size
and frequencies. Consequently, we have displayed alland frequencies. Consequently, we have displayed all
observations and provided a visual description of the shape ofobservations and provided a visual description of the shape of
the distribution.the distribution.

It is often useful to present the stem-and leaf display togetherIt is often useful to present the stem-and leaf display together
with a conventional frequency distribution.with a conventional frequency distribution.
Stem
(Intervals)
Leaves
(Observation)
Frequency
(f)
90-99 2 4 6 8 4
100-109 0 4 6 8 8 8 6
110-119 2 2 4 4 8 8 8 8 8 9
120-129 0 2 2 2 2 4 4 8 8 8 8 8 8 8 8 15
130-139 0 0 0 2 2 4 4 4 4 4 4 8 12
140-149 0 0 2 4 4 6 6
150-159 2 2 4 4 4 4 6 7
160-169 2 2 2
170-179 0 2 2
180-189 0
Total 63

Stem
(Intervals)
Leaves
(Observation)
90-99 2 4 6 8
100-109 0 4 6 8 8 8
110-119 2 2 4 4 8 8 8 8 8
120-129 0 2 2 2 2 4 4 8 8 8 8 8 8 8 8
130-139 0 0 0 2 2 4 4 4 4 4 4 8
140-149 0 0 2 4 4 6
150-159 2 2 4 4 4 4 6
160-169 2 2
170-179 0 2
180-189
From the stem-and-leaf display we can see that theFrom the stem-and-leaf display we can see that the rangerange ofof
measurements is 92 to 172. The measurements in themeasurements is 92 to 172. The measurements in the 120s120s
occur most frequently, withoccur most frequently, with 128128 being the most frequent. Webeing the most frequent. We
can also see which measurements are not represented.can also see which measurements are not represented.
93 95 97

Example
Raw Data:
35, 45, 42, 45, 41, 32, 25, 56, 67,
76, 65, 53, 53, 32, 34, 47, 43, 31

Stem and Leaf Display
First data value = 35
2
3
4
5
6
7
stem
5 leaf

Second data value = 45
2
3
4
5
6
7
5
5

Third data value = 42
2
3
4
5
6
7
5
5 2

2
3
4
5
6
7
5
5 2 5

2
3
4
5
6
7
5
5 2 5 1

2
3
4
5
6
7
5 2
5 2 5 1

2
3
4
5
6
7
5 2
5 2 5 1
5

2
3
4
5
6
7
5 2
5 2 5 1
5
6

2
3
4
5
6
7
5 2
5 2 5 1
5
6
7

2
3
4
5
6
7
5 2
5 2 5 1
5
6
7
6

2
3
4
5
6
7
5 2
5 2 5 1
5
6
7 5
6

2
3
4
5
6
7
5 2
5 2 5 1
5
6 3
7 5
6

2
3
4
5
6
7
5 2
5 2 5 1
5
6 3 3
7 5
6

2
3
4
5
6
7
5 2 2
5 2 5 1
5
6 3 3
7 5
6

2
3
4
5
6
7
5 2 2 4
5 2 5 1
5
6 3 3
7 5
6

2
3
4
5
6
7
5 2 2 4
5 2 5 1 7
5
6 3 3
7 5
6

2
3
4
5
6
7
5 2 2 4
5 2 5 1 7 3
5
6 3 3
7 5
6

2
3
4
5
6
7
5 2 2 4 1
5 2 5 1 7 3
5
6 3 3
7 5
6

Stem and Leaf Display with Leaves
Rearranged
2
3
4
5
6
7
1 2 2 4 5
1 2 3 5 5 7
5
3 3 6
5 7
6

0
5
10
15
20
25
N
one
Prim
ary
Interm
ediate
SeniorH
igh
TechnicalSchool
Education Level
Percentage(%)
Bar ChartsBar Charts
Typically used for displaying categorical or qualitativeTypically used for displaying categorical or qualitative
(nominal or ordinal) data like ethnicity, sex, and(nominal or ordinal) data like ethnicity, sex, and
treatment category. The various categories aretreatment category. The various categories are
represented along the horizontal axis.represented along the horizontal axis.

0
5
10
15
20
25
N
one
Prim
ary
Interm
ediate
SeniorH
igh
TechnicalSchool
Education Level
Percentage(%)
They may be arranged alphabetically, by frequencyThey may be arranged alphabetically, by frequency
within a category, or on some other rational basis.within a category, or on some other rational basis.

0
5
10
15
20
25
N
one
Prim
ary
Interm
ediate
SeniorH
igh
TechnicalSchool
Education Level
Percentage(%)
To prevent any impression of continuity, it isTo prevent any impression of continuity, it is
important that all the bars be of equal width andimportant that all the bars be of equal width and
separate.separate.

0
5
10
15
20
25
N
one
Prim
ary
Interm
ediate
SeniorH
igh
TechnicalSchool
Education Level
Percentage(%)
Male
Female

It is essential that the scale on the vertical axis begin at zero.It is essential that the scale on the vertical axis begin at zero.
When you use a change in scale, warn the viewer by using theWhen you use a change in scale, warn the viewer by using the
squiggle or broken bars on the changed axis as shown insquiggle or broken bars on the changed axis as shown in
Figure. Sometimes, if a single bar is unusually long, the bar length isFigure. Sometimes, if a single bar is unusually long, the bar length is
compressed with a squiggle in the bar itself.compressed with a squiggle in the bar itself.

3-D presentation of Bar chart3-D presentation of Bar chart
0
2
4
6
8
10
12
14
16
18
20
None
Primary
Intermediate
Senior High
Technical School
Male
Female
Percentage(%)

Pareto Chart: Education levels of females from the Honolulu Heart StudyPareto Chart: Education levels of females from the Honolulu Heart Study
0
2
4
6
8
10
12
14
Prim
ary
N
one
Interm
ediate
SeniorH
ighTechnicalSchool
Education level
Frequency
Pareto ChartPareto Chart
A Pareto chart is a graph in which the bar height represents frequency of anA Pareto chart is a graph in which the bar height represents frequency of an
event or categories in decreasing order of frequency of occurrence. The bars areevent or categories in decreasing order of frequency of occurrence. The bars are
arranged from left to right according to decreasing height.arranged from left to right according to decreasing height.

Time plotTime plot
A time plot is a graph display how data change over time. To make aA time plot is a graph display how data change over time. To make a
time plot, we put time on the horizontal scale and the variable beingtime plot, we put time on the horizontal scale and the variable being
measured on the vertical scale. In a basic we connect the datameasured on the vertical scale. In a basic we connect the data
points by lines. It is best if the units of time are consistent in a givenpoints by lines. It is best if the units of time are consistent in a given
plot. For instance, measurements taken every day should not beplot. For instance, measurements taken every day should not be
mixed on the same plot with data taken every week.mixed on the same plot with data taken every week.
Example
How does average height for boys changes as the boy gets older?
According to Physician’s Handbook, the heights at the different ages are as
follows: Age (year) Height (inches)
0.5 26
1 29
2 33
3 36
4 39
5 42
6 45
7 47
8 50
9 52
10 54
11 56
12 58
13 60
14 62

20
25
30
35
40
45
50
55
60
65
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Age (year)
Height(inches)
Time PlotTime Plot
Age (year) Height (inches)
0.5 26
1 29
2 33
3 36
4 39
5 42
6 45
7 47
8 50
9 52
10 54
11 56
12 58
13 60
14 62

Primary; 13;
35%
None; 10; 27%
Intermediate;
8; 22%
Senior High;
4; 11%
Technical
School; 2; 5%
Pie Charts or circle graphsPie Charts or circle graphs
A pie graphA pie graph oror pie chartpie chart presents the distribution of cases in the form of a circle.
The relative size of each slice of the pie is equal to the proportion of cases within
the category represented by the slice. It can be used to displayIt can be used to display eithereither qualitativequalitative
oror quantitative dataquantitative data..

A pie graph presents the distribution of
cases in the form of a circle.
The relative size of each slice of the pie is
equal to the proportion of cases within the
category represented by the slice.

To construct a pie chart for the frequency distribution, construct a tableTo construct a pie chart for the frequency distribution, construct a table
that givesthat gives angle sizesangle sizes for each category. The 360for each category. The 360oo
inin aa circle arecircle are
divided into portions that are proportional to the category sizes .divided into portions that are proportional to the category sizes .
Class Interval
Relative
frequency
Angle size
90-109 0.14 360 X 0.14 = 50.4
110-129 0.41 360 X 0.41 = 147.6
130-149 0.27 360 X 0.27 = 97.2
150-169 0.08 360 X 0.8 = 28.8
170-189 0.05 360 X 0.5 = 18
190-209 0.05 360 X 0.5 = 18
Frequency Table for systolic blood pressure of Smokers
Constructing a pie chartConstructing a pie chart

90 -109
14 %
110 -129
41 %
130 -149
27 %
150 -169
8%
170 -189
5%
190 -209
5%
0%
Pie Chart presentation of systolic blood pressure of SmokersPie Chart presentation of systolic blood pressure of Smokers

Class
(Blood Type) Frequency
Relative
Frequency Angle Size
A 5 0.2 360 X 0.2 = 72
B 8 0.32 360 X 0.32 115.2
O 8 0.32 360 X 0.32 = 115.2
AB 4 0.16 360 X 0.16 = 57.6
Example
A
20%
B
32%
O
32%
AB
16% A
20%
B
32%
O
32%
AB
16%
Pie Chart presentations of blood groupsPie Chart presentations of blood groups

2 organizing and displaying data

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to 2 organizing and displaying data

Similar to 2 organizing and displaying data (20)

More from Lama K Banna

More from Lama K Banna (20)

Recently uploaded

Recently uploaded (20)

2 organizing and displaying data