Final answer:
To make x the median of the given data set, x must be ordered alongside other values and placed in the middle position. Since the list has 10 numbers, x must be the average of the 5th and 6th number after arranging all values in ascending order. Hence, x should be 31.
Step-by-step explanation:
What Value of x Will Make It the Median?
To find the value of x that makes it the median of the data set {20, 25, 32, 45, 40, 30, 45, x, 26, 28}, we first need to order the data from smallest to largest. Once ordered, the median will be the average of the 5th and 6th numbers because there are 10 numbers in total, making the median position between the two middle numbers in an ordered list.
Step 1: Arrange the data in ascending order without x: 20, 25, 26, 28, 30, 32, 40, 45, 45.
Step 2: Find the positions for the 5th and 6th numbers; these are 30 and 32.
Step 3: If x is to be the median, it must be the average of 30 and 32; thus, x should be (30 + 32) / 2 = 31.
Therefore, the value of x must be 31 for x to be the median of the given data set.