Question

the following data represent the amount of time (in minutes) a random sample of eight students took to complete the online portion of an exam in a particular statistics course. compute the mean, median, and mode time. 58.3, 75.7, 92.4, 111.7, 128.4, 93.6, 94.7, 116.1 compute the mean exam time. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the mean exam time is 97.74 (round to two decimal places as needed.) b. the mean does not exist. compute the median exam time. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the median exam time is (round to two decimal places as needed.) b. the median does not exist.

Explanation:

Step1: Order the data

First, we need to order the given data set from smallest to largest. The data is: 58.3, 75.7, 92.4, 93.6, 94.7, 111.7, 116.1, 128.4.

Step2: Find the middle values

Since there are 8 (an even number) data points, the median will be the average of the two middle numbers. The two middle numbers are the 4th and 5th values in the ordered list. The 4th value is 93.6 and the 5th value is 94.7.

Step3: Calculate the median

To find the median, we take the average of these two numbers. The formula for the average of two numbers \(a\) and \(b\) is \(\frac{a + b}{2}\). So we calculate \(\frac{93.6 + 94.7}{2}\).
First, add 93.6 and 94.7: \(93.6+94.7 = 188.3\).
Then divide by 2: \(\frac{188.3}{2}=94.15\).

Answer:

The median exam time is 94.15 (A. The median exam time is 94.15 (Round to two decimal places as needed.))