Question

blocking refers to the idea that the variability in a variable can be reduced by segmenting the data by some other variable. the data in the accompanying table represent the recumbent length (in centimeters) of a sample of 10 males and 10 females who are 40 months of age. complete parts (a) through (d).
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(a) determine the standard deviation of recumbent length for all 20 observations.
6.08 cm (round to two decimal places as needed.)
(b) determine the standard deviation of recumbent length for the males.
5.54 cm (round to two decimal places as needed.)
(c) determine the standard deviation of recumbent length for the females.
5.60 cm (round to two decimal places as needed.)
(d) what effect does blocking by gender have on the standard deviation of recumbent length for each gender?
a. the standard deviation is lower for each group than it is for the groups combined.
b. the standard deviation is higher for each group than it is for the groups combined.
c. the standard deviation for each group is the same as it is for the groups combined.

Explanation:

Compare the combined standard deviation (6.08 cm) to the standard deviations of the male (5.54 cm) and female (5.60 cm) groups. Both group standard deviations are lower than the combined value, which matches the effect of blocking reducing variability within segments.

Answer:

A. The standard deviation is lower for each group than it is for the groups combined.