Question

Find the mean of the following distribution.

x 5 10 15 20 25

y 4 12 20 28 36​

Answer 1

Answer:

 XMid point (x) Frequency (F) i=class  interval width A=22.5 Assumed mean u=ix−A fu0-5 2.5 3 5 22.5 -4 -12 5-10 7.5 5 5 22.5 -3 -15 10 -1512.5 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+105172×5

=22.5+8.19

=30.69 ≈ 31