Question

The mean heights of six fifth grade students is 60.8 inches and the standard deviation is 2.25. A year later each of the six students, now in 6^th grade, has grown exactly two inches. What is the new mean and standard deviation of these six sixth grade students?

Answer 1

Given:

Mean = 60.8 inches and standard deviation = 2.25, change in height = 2inches

Let a = any constant and x = height of students.

Mean ( x+ a) = a+ mean (x)

Mean(x+2) = 2 + mean (x)   =2 + 60.8

New mean for sixth grade = 62.8

If any constant is added in all values, we also add that constant value to mean.

Standard deviation (x + a) = 0 + standard deviation (x)

Standard deviation (x + 2) = standard deviation (x) = 2.25

New standard deviation for sixth grade students = 2.25

There is no effect in standard deviation if we add any constant to data values.