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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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