Question

Calvin found the midrange for a set of numbers to be 32.5. This set of numbers was: 38, 16, 25, 33, 42, ? The ? represents a value missing from the data set. Which of the following could be this missing value?

a) 28
b) 29
c) 30
d) 31

Answer 1

The missing number in the sequence that would result in a midrange of 32.5 is 27, which is not listed among the given options. Therefore, there seems to be an error as none of the provided choices can yield the stated midrange.

Step-by-step explanation:

The question revolves around the concept of midrange in statistics, which is calculated by taking the average of the highest and lowest numbers in a set. To find the missing number in the sequence which results in a midrange of 32.5, we take the known highest number in the set, 42, and the known lowest number, 16. The sum of these two numbers is 58, and to find the midrange, this sum is divided by 2, giving us 29 as the midrange (58/2 = 29). However, since we are given that the actual midrange is 32.5, there must be a mistake in the calculation due to a missing number. To solve for the missing number, we can set up the equation 32.5 = (16 + missing number + 42) / 2. When solved, this equation indicates that the missing number is 27. Among the options given, none precisely match this value, but we can identify which one of them (28, 29, 30, 31) is likely to be incorrect by considering their impact on the known midrange.