Question

17 mark for review data set a 22 23 24 25 26 the dot - plot represents the 15 values in data set a. data set b is created by adding 56 to each of the values in data set a. which of the following correctly compares the medians and the ranges of data sets a and b? a the median of data set b is equal to the median of data set a, and the range of data set b is equal to the range of data set a. b the median of data set b is equal to the median of data set a, and the range of data set b is greater than the range of data set a. c the median of data set b is greater than the median of data set a, and the range of data set b is equal to the range of data set a. d the median of data set b is greater than the median of data set a, and the range of data set b is greater than the range of data set a.

Explanation:

Step1: Find the median of data - set A

Data - set A has 15 values. The median is the 8 - th value when the data is arranged in ascending order. Counting the dots from left to right in the dot - plot, the median of data - set A is 23.

Step2: Create data - set B

Data - set B is created by adding 56 to each value in data - set A. So the median of data - set B is \(23 + 56=79\). Since \(79>23\), the median of data - set B is greater than the median of data - set A.

Step3: Find the range of data - set A

The range of a data - set is the difference between the maximum and minimum values. In data - set A, the minimum value is 22 and the maximum value is 26. So the range of data - set A is \(26 - 22 = 4\).

Step4: Find the range of data - set B

When we add 56 to each value in data - set A to get data - set B, the minimum value of data - set B is \(22 + 56=78\) and the maximum value of data - set B is \(26+56 = 82\). The range of data - set B is \(82 - 78=4\), which is equal to the range of data - set A.

Answer:

C. The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.