MEAN DEVIATION

What is mean deviation?
The mean deviation is the first measure
of dispersion that we will use that
actually uses each data value in
its computation. It is the mean of the
distances between each value and the
mean. It gives us an idea of how spread
out from the center the set of values is.

How can we use mean
deviation in real life?
 Investments
120
100
80
WONDERLAND

60

NEVERLAND

40

FANTASIA

20
0
JANUARY

FEBRUARY

MARCH

APRIL

88.
WONDERLAND = 85+85+89+95/4 = 5
MEAN DEVIATION = 3.5
NEVERLAND = 75+75+80+85=/4 =
MEAN DEVIATION = 3.75

FANTASIA = 87+90+96+97/4=
MEAN DEVIATION = 4

78.75

92.
5

Formula for
Mean Deviation:
(ungrouped data)

MD
Where,
μ = mean

x
n
x = each value

N = number of values

Mean Deviation
-The mean of the distances of
each value from their mean.

Three steps on finding the mean:
1) Find the mean of all values.

2) Find the distance of each value
from that mean.
3) Find the mean of those distances.

Step 2: Find the distance of each
vaue from the mean.
Value

Distance
from 9

3

6

6

3

6

3

7

2

8

1

11

2

15

6

16

7

6+3+3+2+1 = 2+6+7
15 = 15
It tells us how far, on average, all values
are from the middle.

Exercises :
1) A booklet has 12 pages with the
following numbers of words:
271, 354, 296, 301, 333, 326, 285,
298, 327, 316, 287 and 314
What is the mean deviation of the
number of words per page?

Step 1:
Find the mean.
Raw Data:
271, 354, 296, 301, 333, 326, 285,
298, 327, 316, 287, 314
271 354

296

301 333

326

285

298

327

12

30
9
2/22/2014

316

287

314

Step 2: Find the
Absolute Deviations.
x

x

271
354
296
301
333
326
285
298
327
316
287
314

38
45
13
8
24
17
24
11
18
7
22
5
x

232

Step 3: Find the
Mean Deviation
M .D .

x

232

N

12

19.33

Formula for
Mean Deviation:
(grouped data)

f x

MD
Where,
μ = mean

f
x = each value

f = frequency

Three steps on finding the mean:
1) Find the mean by using the formula
fx
f

2) Solve for x
and multiply it to
the frequency of each class. Find the

f x
3) Divide the answer of
the
f

to

Step 1: Find the mean by using the given
formula:

fx
x

f

0
1
2
3
4
5
6

4
12
8
2
1
2
1

f

fx
0
12
16
6
4
10
6

f

30

fx

So,

fx
f
54

54
30

1.8

Step 2: Complete the table.
x

f

fx

0
1
2
3
4
5
6

4
12
8
2
1
2
1

0
12
16
6
4
10
6

f

30

fx

x

f x

1.8
0.8
0.2
1.2
2.2
3.2
4.2
54

7.2
9.6
1.6
2.4
3.3
6.4
4.2
f x

33 . 6

Step 3: Divide the answer of
to the
f
summation of
f x

33 . 6
f

1 . 12

30

Mean Deviation =

1.12

Exercises :
The children in a class did a survey
of the number of siblings (brothers
and sisters) each of them had. The
results are recorded in the
following table. Calculate the mean
deviation.

Step 1: Find the mean by using the given
formula:

fx
x

f

0
1
2
3
4
5
6
7
8
9

3
6
8
5
4
2
1
0
0
1

f

fx
0
6
16
15
16
10
6
0
0
9

f

30

fx

So,
fx

78

f

30

2.6
78

Step 2: Complete the table.
x

f

fx

0
1
2
3
4
5
6
7
8
9

3
6
8
5
4
2
1
0
0
1

0
6
16
15
16
10
6
0
0
9

f

30

fx

x

f x

2.6
1.6
0.6
0.4
1.4
2.4
34
4.4
5.4
6.4

78

7.8
9.6
4.8
2.0
5.6
4.8
3.4
0
0
6.4

f x

44 . 4

Step 3: Divide the answer of
to the
f
summation of
f x

44 . 4
f

1 . 48

30

Mean Deviation =

1.4
8

MEAN DEVIATION

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