Question

88 multiple choice a furniture company makes couches of differing dimensions. the production team is ordered to increase the length of every couch they make by 3 inches. which statement about the lengths of the couches 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 couches produced will increase by 3 inches. b the average length of the couches produced will increase by 6 inches. c the median length of the couches produced will increase by 3 inches.

Explanation:

Step1: Recall measure - of - center property

Adding the same number to each data - point increases measures of center (mean, median) by that number.

Step2: Analyze each option

• Option A: Range is a measure of dispersion. Adding 3 inches to each length does not change the range. So, this option is incorrect.
• Option B: Since 3 inches is added to each length, the average (mean) length will increase by 3 inches, not 6 inches. So, this option is incorrect.
• Option C: Median is a measure of center. When 3 inches is added to each length of the couches, the median length will increase by 3 inches. This option is correct.

Answer:

C. The median length of the couches produced will increase by 3 inches.