Question

Calculate standard deviation and its coefficient class
0-5 5-10 10-15. 15-20. 20-25. 25-30.
4. 6. 10. 16. 12. 8
30-35
4​

Answer 1

Answer:

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Class 11

>>Economics

>>Measures of Central Tendency

>>Arithmetic Mean in Statistics

>>Marks0 - 5 5 - 10 10 - 15 15 - 20 20 - 2

Question

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Marks 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50

Frequency 3 5 7 8 10 11 14 19 15 13

For the following distribution, find the mean using step deviation method. (Round off your answer to the nearest whole number)

Medium

Solution

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Correct option is B)

X Mid point (x) Frequency (F) i=class interval width A=22.5 Assumed mean u=

i

x−A

fu

0-5 2.5 3 5 22.5 -4 -12

5-10 7.5 5 5 22.5 -3 -15

10 -15 12.5 7 5 22.5 -2 -14

15-20 17.5 8 5 22.5 -1 -8

20-25 22.5=A 10 5 22.5 0 0

25-30 27.5 11 5 22.5 1 11

30-35 32.5 14 5 22.5 2 28

35-40 37.5 19 5 22.

5 3 57

40-45 42.5 15 5 22.5 4 60

45-50 47.5 13 5 22.5 5 65

Σf=105 Σfu=172

The formula used for arithmetic mean of grouped data by step deviation method is,

X

=A+

∑f

∑fu

×i

A= Assumed mean of the given data

∑ = Summation of the frequencies given in the grouped data

∑fu = Summation of the frequencies and deviation of a given mean data

u=

i

(x−A)

i= Class interval width

X

= arithmetic mean

X

=22.5+

105

172

×5

=22.5+8.19

=30.69 ≈ 31

Explanation:

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