Video: Finding Missing Data Points given the Mean

A student’s mean score in four tests is 35 marks. After he takes a fifth test, his mean score increases to 37 marks. What was his score on the fifth test?

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Video Transcript

A student’s mean score in four tests is 35 marks. After he takes a fifth test, his mean score increases to 37 marks. What was his score on the fifth test?

So we know that, originally, a student’s mean score on four tests is 35 marks. We can let the four tests be 𝑎, 𝑏, 𝑐, and 𝑑. To find the average of four tests, we would add them together and divide by four, since they’re four tests. And we know what that mean was. It was 35.

Then it says he takes a fifth test, and after that, his average is now 37. So since there are five tests, we would have to divide by five. So we want to solve for that fifth test mark, the score of that. So we will be solving for 𝑒. We can use this first equation to help us solve in the second equation.

First, let’s begin by getting rid of the denominator, so multiplying both sides of the equation by four. This means the fours cancel on the left, and 𝑎 plus 𝑏 plus 𝑐 plus 𝑑 would be equal to 35 times four, which is 140. So what we can do is replace 𝑎, 𝑏, 𝑐, and 𝑑, all of them added together, with 140 in the second equation.

So now to solve for 𝑒, we need to multiply both sides of the equation by five. And we have that 140 plus 𝑒 is equal to 185. So to solve for 𝑒, we subtract 140 from both sides of the equation and find that 𝑒 is equal to 45. So this means that his score on the fifth test would’ve been 45, which makes sense. If his original average was 35 and we would want to increase our average, our next test score would have to be relatively high compared to the others.

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