Statistics

Statistics
Data
6

5

4

3

2

1

0

What is an average?
An average is a measure of the "middle" value of a
set of data.

Mode, Mean, and Median, are all types of averages.

They can be used to help summarise a group of data.

WALT…

…understand what the Mode is
and how to identify it in data.

Definition of Mode
• The “mode” for a set of data is the number (or item)
that occurs most frequently.
• Sometimes data can have more than one mode. This
happens when two or more numbers (or items)occur an
equal number of times in the data.
• A data set with two modes is called bimodal.
• A data set with 3 modes is called Trimodal
• It is also possible to have a set of data with no mode.

How to find the Mode.
 Mode is the most common number
 Put the numbers in order
 Choose the number that appears the
most frequently.
Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6
Put in order: 1, 2, 3, 3, 4, 5, 5, 5, 6, 6

The class modal shoe size is 5.

Find the mode in this data set
Class high jump heights (in metres)

1.05, 1.10, 1.05, .95, .85,1.05, 1.10,
1.20,
.95, 1.25, 1.30, .75, .80, .90,

.75, .80, .85, .90, .95,.95, 1.05,1.05,
1.05, 1.10, 1.10, 1.20, 1.25, 1.30
The mode is 1.05m

Mode of non-numerical data
Red, green, blue, red, blue, yellow, re
d, pink, green, white.

Red, red, red, blue, blue, green, green
, yellow, pink, white.

Mode = red

What is the mode in this data?
Icecream
10
9
8
7
6
5
4 Icecream
3
2
1
0
strawberry vanilla chocolate neopolitan

Bar graph data

Mode = Neopolitan

Bimodal and trimodal
Bimodal
Data Set = 2, 5, 2, 3, 5, 4, 7
2, 2, 3, 4, 5, 5, 7
Modes = 2 and 5
Trimodal
Data Set = 2, 5, 2, 7, 5, 4, 7
2, 2, 4, 5, 5, 7, 7
Modes = 2, 5, and 7

Example
Data Set= 3, 5, 6, 4, 7, 8, 9, 2, 1, 0

What is the mode?
0,1,2,3,4,5,6,7,8,9
Is the mode = 0?

Mode = no mode

When might the Mode be used?
 The mode can be useful for dealing with
categorical data. For example, if a sandwich shop
sells 10 different types of sandwiches, the mode
would represent the most popular sandwich.
 The mode can be useful for summarising survey
data.
 The mode can be useful for election votes.

Averages
 What other ways can we calculate
the average of a set of data?

 We can use the Mean to give us an
average of numerical data.

WALT…

understand what the Mean is and how
to identify it in data.

Definition of the Mean
 The „Mean‟ is the „Average‟ value of numerical
data.
 The Mean (or average) is found by adding all
scores together and dividing by the number of
scores.

Example

 Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6
 Add up the numbers:
 3 + 5 + 5 + 6 + 4 + 3 + 2 + 1 + 5 + 6 = 40
 Divide by how many numbers:
 40 ÷ 10 = 4
 The class mean shoe size is 4

Find the Mean

1.05, 1.10, 1.05, .95, .85,1.05, 1.10, 1.20, .95, 1.2
5, 1.30, .75, .80, .90,

1.05 + 1.10 + 1.05 +.95 + .85 +1.05 + 1.10 +
1.20 + .95 + 1.25 + 1.30 + .75 + .80 + .90 =
14.3m

Mean = 14.3 divided by the number of people that
jumped (14)
14.3 ÷ 14 = 1.02m

Population of NZ Cities
1600000
1400000
1200000
1000000
800000
600000
400000 Population
200000
0

What is the mode? What is the mean?

Work it out
 Mode = most common – 390,000 is the mode of
the population of the NZ Cities on the graph.
 Mean = the average population of the NZ cities
on the graph –

200,000 + 60,000 + 390,000 + 390,000 + 125,000
+ 1355,000 = 2520,000

Mean = 2520,000 ÷ 6 = 420,000

When to use the mean…
 The mean can give a good average value when
the data is fairly evenly distributed as in the high
jump heights.

1.05 + 1.10 + 1.05 +.95 + .85 +1.05 + 1.10 +
1.20 + .95 + 1.25 + 1.30 + .75 + .80 + .90 =
14.3m
Mean = 14.3 divided by the number of people that
jumped (14)
14.3 ÷ 14 = 1.02m

However
 It is not always suitable to use the
mean to get an average of data
when there is a huge variation in
data.

Example
Population of NZ Cities
1600000
1400000
1200000
1000000
800000
600000
400000 Population
200000
0

What is an average?
,
.
An average is a measure of the "middle" value of a
set of data.

Mode, Mean, and Median, are all types of averages.

They can be used to help summarise a group of data.

Recap
Definition of Mode –
The “Mode” for a set of data is the
number (or item) that occurs most
frequently.
Definition of Mean –
The “Mean” is the „Average‟ value of
numerical data.

Example
.
1.05, 1.10, 1.05, .95, .85,1.05, 1.05,1.
20, .95, .50, .80, .65, 1.05, 1.10,.95
.95, 1.25, 1.30, .75, .80, .90, 1.00, 1.1
0, 1.15, 1.25, 1.10, 1.10, 1.15
What is the mode?
What is the mean?

Answers

Mode = 1.05 and 1.10

Mean = 1.00

WALT…

..understand what the Median is and
how to identify it in data.

Definition of Median
 The Median is the middle value when
numbers are put in order.
 To find the Median, place the numbers in
numerical order and find the middle
number.
 If the total number of values in the
sample is even, the median is calculated
by finding the mean of the two values in
the middle.

Find the median…
Room 19 test scores
56%, 48%, 76%, 78%, 85%, 77%, 91%, 77%, 73
%, 88%, 69%, 67%, 58%, 64%, 88%, 89%, 87%,
83%, 73%, 74%, 92%, 69%, 80%, 80%, 75%, 72
%.

In order –
48%, 56%, 58%, 64%, 67%, 69%, 69%, 72%, 73
%, 73%, 74%, 75%, 76%, 77%, 77%, 78%, 80%,
80%, 83%, 85%, 87%, 88%, 88%, 89%, 91%, 92
%,

Find the mode
How many children in your family?
12

10

8

6
Quantity
4

2

0
Two Three Four Five Six

Find the Mean
.
. How many children in your family?
12

10

8

6
Quantity
4

2

0

To find the mean…
(10 x 2) + (10 x 3) + (5 x 4) + (3 x 5)
+ (1 x 6) = 91

91 ÷ 29 = 3.13 rounded to 3

Mean = 3

Find the. median
 . How many children in your family?
12

10

8

6
Quantity
4

2

0

To find the median…
 Put the numbers in order…
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3,
3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6.

The Median = 3

Range
 Range is the gap from the biggest to
smallest value.
 Put the numbers in order
 Take the smallest number away from
the largest.
Class shoe sizes: 3, 5, 5, 6, 4, 3, 2, 1, 5, 6
Put in order: 1, 2, 3, 3, 4, 5, 5, 5, 6, 6
Subtract smallest from largest: 6 – 1 = 5
Range: 5

When should you use the
Mean, Mode, or Median?

 Use the mean for data which is fairly
evenly distributed.
 Use the median for data which has
extreme differences in scores.
 Use the mode in categorical data
where the original scores are known.

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