Question

which data set would you expect to have the highest standard deviation: heights (lengths) of newborn infants, heights of all elementary - school children, or heights of first - grade boys?
choose the correct answer below.
a. the heights of newborn infants, since it has the largest range.
b. the heights of first - grade boys, since it has the smallest range.
c. the heights of all elementary - school children, since it has the smallest range.
d. the heights of all elementary - school children, since it has the largest range.
e. the heights of newborn infants, since it has the smallest range.
f. the heights of first - grade boys, since it has the largest range.

Explanation:

Standard deviation measures the spread of data. A larger range (difference between maximum and minimum values) generally implies a larger spread. Among the three data - sets (newborn infants' heights, all elementary - school children's heights, first - grade boys' heights), all elementary - school children have a wider age range (from kindergarten to 5th or 6th grade in some systems). This wider age range leads to a greater variety in heights (as children grow over several years), resulting in a larger range of heights. Since a larger range is associated with a larger standard deviation (assuming a somewhat symmetric distribution, which is a reasonable assumption for human height distributions), the data - set of all elementary - school children's heights is expected to have the highest standard deviation.

Answer:

D. The heights of all elementary - school children, since it has the largest range.