The mean deviation is a measure of how spread out values are from the average. It is calculated by: 1) Finding the mean of all values. 2) Calculating the distance between each value and the mean. 3) Taking the average of those distances. This provides the mean deviation, which tells us how far on average values are from the central mean. Examples show calculating mean deviation for both grouped and ungrouped data sets.

1. Mean
Deviation

2. 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.

3. How can we use mean
deviation in real life?
 Investments
120
100
80
WONDERLAND
60
NEVERLAND
40
FANTASIA
20
0
JANUARY
FEBRUARY
MARCH
APRIL

4. 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

5. Formula for
Mean Deviation:
(ungrouped data)
MD
Where,
μ = mean
x
n
x = each value
N = number of values

6. 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.

8. 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.

9. 3.7
5

10. 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?

11. 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

12. 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

13. Step 3: Find the
Mean Deviation
M .D .
x
232
N
12
19.33

14. Formula for
Mean Deviation:
(grouped data)
f x
MD
Where,
μ = mean
f
x = each value
f = frequency

15. 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

16. 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

17. 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

18. Step 3: Divide the answer of
to the
f
summation of
f x
33 . 6
f
1 . 12
30
Mean Deviation =
1.12

19. 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.

20. 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

21. 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

22. Step 3: Divide the answer of
to the
f
summation of
f x
44 . 4
f
1 . 48
30
Mean Deviation =
1.4
8