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Chapter 32: Statistics – Exercise 32.1

Statistics – Exercise – 32.1 – Q.1(i)

First arrange the given numbers in ascending order writer these numbers in ascending order

3011, 2780, 3020, 2354, 3541, 4150, 5000

we get 2354, 2780, 3011, 3020, 3541, 4150, 5000

Clearly, the middle number is median, 3020

Calculation of mean Deviations

xi |di| = |xi - 3020|
3011 9
2780 240
3020 0
2354 666
3541 521
4150 1130
5000 1980
Total di = Σ|xi - 30200|=4546

 

 

Statistics – Exercise – 32.1 – Q.1(ii)

Clearly, the middle observations are 46 and 48. So, median = 47

35
38
42
44
46
48
54
55
63
70

We have,

Σ|xi - 47| = Σdi = 86

 

Statistics – Exercise – 32.1 – Q.1(iii)

Arranging the observations in ascending order of magnitude, we have

30
34
38
40
42
44
50
51
60
66

Clearly, the middle observations are 42 and 44. So, median = 43

Σ|xi - 43| = Σdi = 87

 

Statistics – Exercise – 32.1 – Q.1(iv)

Arranging the observations in ascending order of magnitude, we have

22
24
25
27
28
29
30
31
41
42

Clearly, the middle observation are 28 and 29. So median = 28.5

Calculation of mean Deviation

X-values Deviation from Median
22 6.5
24 4.5
30 1.5
27 1.5
29 0.5
31 2.5
25 3.5
28 0.5
41 12.5
42 13.5
Total 47

We have,

Σ|xi - 28.5| = Σdi = 47

 

Statistics – Exercise – 32.1 – Q.1(v)

Arranging the observations in ascending order of magnitude, we have

34
38
42
44
47
48
53
55
63
70

Clearly, the middle observation is, So, median = 47.5

Calculation of Mean Deviation

X-values Deviation from Median
38 9.5
70 22.5
48 0.5
34 13.5
63 15.5
42 5.5
55 7.5
44 3.5
53 5.5
48 0.5
Total 84

We have,

Σ|xi - 47.5| = Σdi = 84 

 

Statistics – Exercise – 32.1 – Q.2(i)

Calculation of Mean Deviation

X - values Deviation from mean
4 6
7 3
8 2
9 1
10 0
12 2
13 3
17 7
Total 24

We have,

Σ|xi - 10| = Σi = 24 

 

Statistics – Exercise – 32.1 – Q.2(ii)

Calculation of Mean Deviation

X-values Devlation From Mean
13 1
17 3
16 2
14 0
11 3
13 1
10 4
16 2
11 3
18 4
12 2
17 3
Total 28

We have,

Σ|xi - 14| = Σdi = 28 


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