Question

calculate the arithmatic mean from the following data using step deviation method ; expenditure (Rs) no . of students 5-9 1 10-14 3 15-19 5 20-24 4 25-29 2

Answer 1

Answer:

Find out mean deviation and its coefficient of the following data:

Items 5 10 15 20 25 30 35 40

Frequency 8 16 18 22 14 9 6 7

ANSWER:

Items (X) Frequency (f) fX Deviation from Mean

∣∣X−X∣∣= ∣∣dX∣∣ f∣∣dX∣∣

5

10

15

20

25

30

35

40 8

16

18

22

14

9

6

7 40

160

270

440

350

270

210

280 15.2

10.2

5.2

0.2

4.8

9.8

14.8

19.8 121.6

163.2

93.6

4.4

67.2

88.2

88.8

138.6

Σf = 100 Σfx = 2020 Σf∣∣dX∣∣=765.6

(a) Mean (X¯¯¯)=ΣfxΣf=2020100=20.2

(b) Mean deviation from Arithmetic Mean

MDX=Σf∣∣dX∣∣Σf=765.6100=7.656

(c) Coefficient of MDX¯¯¯ =MDXX=7.65620.2=0.379=0.38 approx.