Question

Suppose the following table summarizes the BMI for a population of 8 participants in a weight loss program. Calculate µ and σ.

Participant	BMI
A	32.6
B	31.7
C	26.8
D	29.3
E	25.4
F	33.2
G	29.4
H	26.9

Answer 1

Solution:-

From given that,

Data-32.6,31.7,26.8,29.3,25.4,33.2,29.4,26.9

x	dx=x-A=x-29	dx2
32.6	3.6	12.96
31.7	2.7	7.29
26.8	-2.2	4.84
29.3	0.3	0.09
25.4	-3.6	12.96
33.2	4.2	17.64
29.4	0.4	0.16
26.9	-2.1	4.41
---	---	---
∑x=235.3	∑(dx)=3.3	∑(dx)2=60.35

Mean ˉx=u=∑x/n

=32.6+31.7+26.8+29.3+25.4+33.2+29.4+26.9/8

=235.3/8

=29.4125

ˉx=29.4125 is not an integer, use assumed mean method

A=29

Population Standard deviation σ=√∑dx²-(∑dx)²/n/n

=√60.35-(3.3)²/8/8

=√60.35-1.3613/8

=√58.9888/8

=√7.3736

=2.7154