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.
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.
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