Question

1. kenji earned the test scores below in english class. {79, 91, 93, 85, 86, 88} after his next test, his mean and median scores both change to 88. what does he earn on this test? a 86 b 89 c 91 d 94

Explanation:

Step1: Calculate sum of original scores

The original scores are \(79,91,93,85,86,88\). The sum of these scores is \(79 + 91+93 + 85+86+88=522\). Let the new - score be \(x\). Then the sum of all scores (including the new one) is \(S=522 + x\).

Step2: Use mean formula

The mean of the \(n = 7\) scores (after adding the new score) is \(\bar{x}=\frac{S}{n}\). We know that \(\bar{x}=88\) and \(n = 7\). So, \(\frac{522 + x}{7}=88\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(\frac{522 + x}{7}=88\) by \(7\): \(522+x=88\times7\). Since \(88\times7 = 616\), we have \(522+x=616\). Subtract \(522\) from both sides: \(x=616 - 522=94\).
We can also check the median. The original scores in ascending order are \(79,85,86,88,91,93\). When we add \(94\), the scores in ascending order are \(79,85,86,88,91,93,94\). The median of \(7\) numbers (the middle - number) is the \(4^{th}\) number, which is \(88\).

Answer:

D. 94