Question

1. set a and set b each consist of 5 distinct numbers. the 2 sets contain identical numbers with the exception of the number with the least - value in each set. the number with the least value in set b is greater than the number with the least value in set a. the value of which of the following measures must be greater for set b than for set a?

a. mean only
b. median only
c. mode only
d. mean and median only
e. mean, median, and mode

Explanation:

Step1: Understand the sets

Set A and B have 4 same - value elements, and the smallest value in B is greater than the smallest value in A.

Step2: Analyze the mean

Let the elements of Set A be \(a_1,a_2,a_3,a_4,a_5\) with \(a_1\) being the smallest, and elements of Set B be \(b_1,b_2,b_3,b_4,b_5\) where \(b_1 > a_1\) and \(a_i=b_i\) for \(i = 2,3,4,5\). The mean of Set A is \(\bar{x}_A=\frac{a_1 + a_2+a_3+a_4+a_5}{5}\), and the mean of Set B is \(\bar{x}_B=\frac{b_1 + b_2+b_3+b_4+b_5}{5}\). Since \(b_1>a_1\) and \(a_i = b_i\) for \(i = 2,3,4,5\), \(\bar{x}_B>\bar{x}_A\).

Step3: Analyze the median

Since both sets have 5 (an odd - number) elements, the median is the third - ordered element. As the non - smallest four elements are the same in both sets, the medians of Set A and Set B are equal.

Step4: Analyze the mode

Since the sets have distinct numbers, there is no mode (or mode is not well - defined in the traditional sense for sets of distinct numbers). So, the mode is not greater for Set B.

Answer:

A. Mean only