Author Question: A sample of 13 college professors has a mean age of 30 years and a standard deviation of 5 years. ... (Read 229 times)

burton19126 · **on:** Jun 24, 2018

A sample of 13 college professors has a mean age of 30 years and a standard deviation of 5 years. Suppose that the sample is enlarged to 15 college professors, by including two additional professors that are each 30 years old. Will the standard deviation increase, decrease, or stay the same, and why?

Question 2

The following data represent the number of children in a sample of 10 families from a certain community: 4, 2, 1, 1, 5, 3, 0, 1, 0, and 2.
a. Compute the range.
b. Compute the variance.
c. Compute the standard deviation.
d. Compute the coefficient of variation.
e. Explain why in this case range > variance > standard deviation > coefficient of variation.

mfedorka · **Reply #1 on:** Jun 24, 2018

Answer to Question 1

The new standard deviation will be smaller than the original one because the two new professors' ages don't deviate from the mean, but they add two more observations to the data set, bringing down the average deviation from the mean. The new standard deviation actually is s = 4.643.

Answer to Question 2

a. 5
b. 2.77
c. 1.66
d. 0.87
e. The range is the difference between the largest and smallest observation, which compares the numbers to each other; the variance is in essence the average squared deviation from mean, which compares the numbers to the mean. The standard deviation is less than the variance because it's the square root of a number larger than one. The coefficient of variation is even smaller because the mean is larger than the standard deviation.