1) This document discusses formulas and calculations for mean deviation and mean deviation from the median. It provides examples of calculating mean deviation from the mean and median for both individual and discrete data sets. 2) Mean deviation from the mean is calculated as the sum of the deviations of individual values from the mean, divided by the sample size. Coefficient of mean deviation from the mean is the mean deviation divided by the mean. 3) Median deviation is similarly defined, but uses the median rather than the mean as the point of comparison. Examples are provided to demonstrate calculating mean and median deviation for different data sets.

1. Formula:
M.D from mean =
𝒙−𝒙
𝑵
Coefficient of M.D from mean
𝑴.𝑫
𝑴𝒆𝒂𝒏
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2. Mean deviation
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https://www.mathsisfun.com/data/mean-deviation.html

3. Find the mean deviation from mean of the data given below
Income : 100, 105, 125, 130, 140
Therefore mean 𝒙 =
𝒙
𝑵
=
𝟔𝟎𝟎
𝟓
= 120
Income (X)
100
105
125
130
140
𝒙 = 600
𝒙
120
120
120
120
120
X - 𝒙
- 20
-15
5
10
20
𝒙 − 𝒙
20
15
5
10
20
𝒙 − 𝒙 = 70
M.D from mean =
𝒙−𝒙
𝑵
=
70
5
= 14
C.M.D from mean =
𝑀.𝐷 𝑓𝑟𝑜𝑚 𝑚𝑒𝑎𝑛
𝑀𝑒𝑎𝑛
=
14
120
= 0.12
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Mean deviation – Individual data

4. Mean deviation from mean- Discrete data
Formula :
M. D from mean =
𝑓 𝑥−𝑥
𝑁
Coefficient of M.D from mean =
𝑀.𝐷 𝑓𝑟𝑜𝑚 𝑚𝑒𝑎𝑛
𝑀𝑒𝑎𝑛
Age (in years) 6 8 10 12 14
No. of
students
4 2 5 3 1
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5. • Calculation of M.D from mean its coefficient .
Age (in years) 6 8 10 12 14
No. of students 4 2 5 3 1
f. 𝒙 − 𝒙
3.33
1.33
0.67
2.67
4.67
f. 𝒙 − 𝒙 = 32.01
• Mean (𝒙) =
𝒇𝒙
𝑵
=
140
15
=9.33
Now,
M. D from mean =
𝒇 𝒙−𝒙
𝑵
=
32.01
15
=2.134
C. M.D from mean =
𝑀.𝐷 𝑓𝑟𝑜𝑚 𝑚𝑒𝑎𝑛
𝑀𝑒𝑎𝑛
=
2.134
9.33
= 0.228
Age (x) f
6
8
10
12
14
4
2
5
3
1
N=15
f.x
24
16
50
36
14
𝑓𝑥=140
𝒙
9.33
9.33
9.33
9.33
9.33
𝒙 − 𝒙
3.33
1.33
0.67
2.67
4.67
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6. The following table represents the marks of opt. Maths of class 9
Marks 60 70 80 90 100
Students 10 6 10 3 1
Making table
f. 𝒙 − 𝒙
130
18
70
51
27
f 𝒙 − 𝒙 =296
Mean ( 𝑥) =
𝑓𝑥
𝑁
M.D. from mean =
f 𝒙−𝒙
𝑵
C. M.D from mean =
𝑀..𝐷 𝑓𝑟𝑜𝑚 𝑚𝑒𝑎𝑛
𝑀𝑒𝑎𝑛
=
9.87
73
= 0.14
Marks (X) f
60
70
80
90
100
10
6
10
3
1
N=30
f.x
600
420
800
270
100
𝑓𝑥=2190
=
𝟐𝟏𝟗𝟎
𝟑𝟎
= 73
𝒙
73
73
73
73
73
𝒙 − 𝒙
13
3
7
17
27
=
296
30
= 9.87
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7. M.D from median- individual data
Median Md = value of
𝑁+1
2
𝑡ℎ
term
M.D from median =
𝑥 −𝑀𝑑
𝑁
C.M.D from median =
𝑀.𝐷.𝑓𝑟𝑜𝑚 𝑚𝑒𝑑𝑖𝑎𝑛
𝑀𝑒𝑑𝑖𝑎𝑛
Marks obtained by 10 students in math are given below
100, 80, 90, 70, 70, 60, 50, 30, 40, 40
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8. Marks obtained by 10 students in math are given below
100, 80, 90, 70, 70, 60, 50, 30, 40, 40
Arranging the data in ascending order
𝒙 − 𝑴𝒅
35
25
25
15
5
5
5
15
25
35
𝒙 − 𝑴𝒅 =160
Median (Md) = value of
𝑁+1
2
𝑡ℎ
term
= 5.5th term
=
5𝑡ℎ+6𝑡ℎ
2
th term
=
60 + 70
2
= 65
M.D from median =
𝑥 −𝑀𝑑
𝑁
=
160
10
= 16
C.M.D from median =
𝑀.𝐷.𝑓𝑟𝑜𝑚 𝑚𝑒𝑑𝑖𝑎𝑛
𝑀𝑒𝑑𝑖𝑎𝑛
Marks
30
40
40
50
60
70
70
80
90
100
N = 10
Md
65
65
65
65
65
65
65
65
65
65
X-Md
-35
-25
-25
-15
-5
5
5
15
25
35
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9. M.D from median- discrete data
Median Md = value of
𝑁+1
2
𝑡ℎ
term
M.D from median =
𝑓 𝑥 −𝑀𝑑
𝑁
C.M.D from median =
𝑀.𝐷.𝑓𝑟𝑜𝑚 𝑚𝑒𝑑𝑖𝑎𝑛
𝑀𝑒𝑑𝑖𝑎𝑛
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Age in years 6 8 12 10 20
14Students 5 8 21 5 1

10. Arranging the data in ascending order and making a table for M.D from median
Median(Md) =
𝑁+1
2
𝑡ℎ
term
Age in years 6 8 12 10 20
14Students 5 8 21 5 1
f 𝒙 − 𝑴𝒅
30
32
10
0
8
𝑓 𝑥 − 𝑀𝑑 =80
=
40+1
2
𝑡ℎ
term
= 20.5th term
C.F just greater than 20.5 is 39 and its
corresponding value is 12
So, median (Md) = 12
M.D from median =
𝑓 𝑥 −𝑀𝑑
𝑁
M.D from median =
80
40
= 2
C. M.D from median =
𝑀.𝐷 𝑓𝑟𝑜𝑚 𝑚𝑒𝑑𝑖𝑎𝑛
𝑀𝑒𝑑𝑖𝑎𝑛
=
2
12
= 0.17
Age (x) f
6
8
10
12
20
5
8
5
21
1
C.f
5
5+8=13
13+5=18
18+21 = 39
39+1=40
N=40
Md
12
12
12
12
12
𝒙 − 𝑴𝒅
6
4
2
0
8
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11. JANAK SINGH SAUD
email: saudjanaksingh@gmail.com
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