Question

determine the mean, median, mode, and midrange for this collection of class test scores: 88 82 97 76 79 92 65 84 79 90 75 82 78 77 93 88 95 73 69 89 93 78 60 95 88 72 80 94 88 74 a. mean is 84, median is 82, mode is 82, midrange is 77 b. mean is 82, median is 88, mode is 88, midrange is 77 c. mean is 82.4, median is 88, mode is 82, midrange is 78.5 d. mean is 82.4, median is 82, mode is 88, midrange is 78.5 please select the best answer from the choices provided

Explanation:

Step1: Calculate the mean

First, find the sum of all the scores.

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There are \(n = 30\) scores. The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{2472}{30}=82.4\)

Step2: Find the median

Sort the data in ascending order:
\(60,65,69,72,73,74,75,76,77,78,78,79,79,80,82,82,84,88,88,88,88,88,89,90,92,93,93,94,95,95,97\)
Since \(n = 30\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=15\), \(\frac{n}{2}+1 = 16\). The 15th value is \(82\) and the 16th value is \(82\). Median \(M=\frac{82 + 82}{2}=82\)

Step3: Determine the mode

The mode is the value that appears most frequently. The score \(88\) appears \(5\) times, which is more frequent than other scores.

Step4: Calculate the mid - range

The mid - range \(MR=\frac{\text{Minimum}+\text{Maximum}}{2}\). The minimum value \(x_{\min}=60\) and the maximum value \(x_{\max}=97\). Mid - range \(MR=\frac{60 + 97}{2}=\frac{157}{2}=78.5\)

Answer:

D. Mean is \(82.4\), median is \(82\), mode is \(88\), midrange is \(78.5\)