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. 68.3, 76.7, 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 (round to two decimal places as needed.) b. the mean does not exist.

Explanation:

Step1: Sum all the data values

We have the data points: 68.3, 76.7, 92.4, 111.7, 128.4, 93.6, 94.7, 116.1.
First, we sum them up:
\[

$$\begin{align*} &68.3 + 76.7 + 92.4 + 111.7 + 128.4 + 93.6 + 94.7 + 116.1\\ =&(68.3 + 76.7) + 92.4 + 111.7 + 128.4 + 93.6 + 94.7 + 116.1\\ =&145 + 92.4 + 111.7 + 128.4 + 93.6 + 94.7 + 116.1\\ =&(145 + 92.4) + 111.7 + 128.4 + 93.6 + 94.7 + 116.1\\ =&237.4 + 111.7 + 128.4 + 93.6 + 94.7 + 116.1\\ =&(237.4 + 111.7) + 128.4 + 93.6 + 94.7 + 116.1\\ =&349.1 + 128.4 + 93.6 + 94.7 + 116.1\\ =&(349.1 + 128.4) + 93.6 + 94.7 + 116.1\\ =&477.5 + 93.6 + 94.7 + 116.1\\ =&(477.5 + 93.6) + 94.7 + 116.1\\ =&571.1 + 94.7 + 116.1\\ =&(571.1 + 94.7) + 116.1\\ =&665.8 + 116.1\\ =&781.9 \end{align*}$$

\]

Step2: Divide the sum by the number of data points

There are 8 data points (since it's a sample of eight students). The formula for the mean \(\bar{x}\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 8\) and \(\sum_{i=1}^{n}x_{i}=781.9\).
So, \(\bar{x}=\frac{781.9}{8}\)
\[
\frac{781.9}{8}=97.7375
\]
Rounding to two decimal places, we get \(97.74\).

Answer:

A. The mean exam time is \(97.74\)