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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