Question

A person's metabolic rate is the rate at which the body consumes energy. Metabolic rate is important in studies of weight gain, dieting, and exercise. Here are the metabolic rates of 7 men who took part in a study of dieting. (The units are calories per 24 hours. These are the same calories used to describe the energy content of foods.) 1720 1687 1367 1614 1460 1867 1436 Calculate the mean and standard deviation of the metabolic rates, showing each step in detail.

Answer 1

Let m be mean

Mean= sum/ n

Mean= (1720+1687+1367+1614+1460+1867+1436) / 7

m= 11151 / 7

M= 1593

Mean= 1593

Standard deviation

|x-m|^2

For 1st: |1720-1593|^2=8836

For 2nd: |1687-1593|^2=10201

For 3rd: |1367-1593|^2=51076

For 4th: |1614-1593|^2=441

For 5th: |1460-1593|^2=1689

For 6th: |1867-1593|^2=75076

For 7th: |1436-1593|^2=24649

Summation of |x-m|^2 = 171968

Standard deviation sample formula is:

S.D = sqrt((summation of |x-m|^2) / n-1)

S.D=sqrt(171968/6)

S.D=sqrt(28661.33)

S.D=169.30

Standard deviation is 169.30