Question

Five test scores have a mean (average score) of 90, a median (middle score) of 91 and a mode (most frequent score) of 94. Find the sum of the two lowest test scores.

Answer 1

The sum of the two lowest test scores is 171.

Explanation:

We see that there are 5 test scores, so the median ( middle score ) was not taken to be the average of the two middle scores. It is an element present in the set of five test scores. The mode of course has to be present in the set, but multiple times. If we can figure out how many times this mode is present in the set, it would help us.

As 91 is the middle value, there has to be two above 91. Therefore, as 94 appears the most frequent, is must appear twice.

Now another key thing we need here is the sum of all 5 numbers. Given a mean of 90, 90
`*` 5 = the sum of all 5 numbers = 450. Therefore, the sum of the two lowest test scores should be = 450 - 94 - 94 - 91 = 171 - which is our solution.

Answer 2

171 points.

Explanation:

If five test scores have a mean of 90, all the scores added together will be 5 * 90 = 450.

The middle score is 91, so the other four scores added together will be 450 - 91 = 359.

The mode is higher than the median, so we can assume that the highest two numbers are the same: 94. 94 * 2 = 188. 359 - 188 = 171.

That means that the sum of the two lowest test scores is 171 points.

Hope this helps!