Question

a shoelace company makes shoelaces of differing lengths. the production team is ordered to increase the length of every shoelace they make by 3 centimeters. which statement about the lengths of the shoelaces the company will produce after the change is true? remember: adding same number to every value in a data set increases the measures of center for the data set by the same value. the measures of dispersion are unchanged. a the range of lengths of the shoelaces produced will increase by 3 centimeters. b the average length of the shoelaces produced will increase by 6 centimeters.

Explanation:

Step1: Recall measure - of - center and dispersion rules

Adding the same number to each data - point in a data set affects the measures of center (mean, median, mode) but not the measures of dispersion (range, variance, standard deviation).

Step2: Analyze option A

The range is a measure of dispersion. Since adding 3 cm to each shoelace length does not change the dispersion, the range will not increase by 3 cm. So option A is false.

Step3: Analyze option B

The average (mean) is a measure of center. When we add 3 cm to each shoelace length, the average length of the shoelaces will increase by 3 cm, not 6 cm. So option B is false.
Since the correct rule is that adding 3 cm to each shoelace length will increase the measures of center (like the average) by 3 cm and leave the measures of dispersion (like the range) unchanged, neither of the given options is correct. But if we assume we are only considering the measure - of - center concept for the question's intent, the average length of the shoelaces will increase by 3 cm.

Answer:

Neither A nor B is correct. If considering measure of center only, the average length of the shoelaces will increase by 3 cm.