Question

ari’s teacher says he may have his report grade based on either the mean or the median of his last six test scores. 88%, 73%, 97%, 76%, 90%, 80% which measure of center would best represent ari’s grade? the mean the median both the mean and the median neither the mean nor the median

Explanation:

Step1: Arrange the data in ascending order

First, we arrange the scores \(73\%,76\%,80\%,88\%,90\%,97\%\) in ascending order.

Step2: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Here \(n = 6\), \(x_{1}=73\), \(x_{2}=76\), \(x_{3}=80\), \(x_{4}=88\), \(x_{5}=90\), \(x_{6}=97\).
\(\bar{x}=\frac{73 + 76+80 + 88+90+97}{6}=\frac{504}{6}=84\)

Step3: Calculate the median

Since \(n = 6\) (an even - numbered data set), the median \(M=\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}\). Here \(\frac{n}{2}=3\), \(\frac{n}{2}+1 = 4\).
\(M=\frac{80 + 88}{2}=\frac{168}{2}=84\)

Answer:

both the mean and the median