Video Transcript
Two values are missing from the shown data set. Given that the median is 67, the range is 44, and the data is listed in ascending order, find the missing values. 43, 47, 62, blank, 76, blank.
We know that the median is the middle value when the numbers are listed in ascending or descending order. In this question, we have six values. The third and fourth values will be the middle two numbers. This means that the median will be halfway between the third and fourth number. To find the midpoint of any two numbers, we add the numbers and then divide by two. If we let the first missing number be 𝑥, this gives us 62 plus 𝑥 divided by two. As the median is 67, this expression is equal to 67.
Multiplying both sides of this equation by two gives us 62 plus 𝑥 is equal to 134. Subtracting 62 from both sides of this equation gives us a value of 𝑥 of 72. The first missing number in our list is 72. We could also have worked this out using a number line. The median is 67, and the lower of our two values was 62. These have a difference of five. As 67 needs to be in the middle of our two values, we can add five to this to calculate the missing number. 67 plus five is equal to 72, which confirms our answer for the first missing number.
We are also told in the question that the range is 44. We can calculate the range by subtracting the smallest number from the largest number. Another way of thinking about this is we need to add 44 to the smallest number to find the largest number. 43 plus 44 is equal to 87. To check that 87 is indeed our second missing number, we can subtract 43 from it to give us an answer of 44, which was the range. The two values that are missing from the data set are 72 and 87.
