Two values are missing from the shown data set. Given that the mode is 88, the mean is 55, and the data is listed in ascending order, find the missing values.
We have the values of nine, 38, 50, a missing value, 88, and the last missing value. Since the mode is 88, that means 88 will occur the most often. So far, nine is listed once, 38 is listed once, 50 is listed once, and 88 is listed once. So we need to list 88 one more time so it’s listed the most.
At the moment, we don’t know whether 88 would go in the first empty slot or the second empty slot because it says that these numbers are listed in ascending order, so they’re listed from the smallest number to the largest number. It also states the mean is 55, so the average would be 55.
In order to find the mean, we need to add all the numbers up and then divide by six since there are six numbers. We know that there are two 88s; we just don’t know the last number and we don’t know whether it will go in the last slot or the first empty slot. Now we also know that the mean is actually equal to 55, and then we can solve for our last missing number.
So we can replace the mean with 55. Now to solve, let’s add all of the numbers on the right-hand side of the equation on the numerator. So let’s add nine, 38, 50, 88, and 88 together.
So we have 55 is equal to 273 plus 𝑥 all divided by six. So to solve for 𝑥, we first need to multiply both sides by six. On the left, six times 55 is 330, and on the right, the sixes cancel. Now we need to subtract 273 from both sides of the equation.
That means 𝑥 is equal to 57, so our other missing number for this data set is 57. And since our numbers are listed in ascending order, the 57 will go in the first empty slot and the 88 will go in the last empty slot. Therefore, the missing values are 57 and 88.