Question

find the mean, median, and mode of the data, if possible. if any of these measures cannot be found or a measure does not represent the center of the data, explain why. a sample of seven admission test scores for a professional school are listed below. 9.8 10.1 9.8 10.2 9.8 11.1 11.6

Explanation:

Step1: Find the Mean

The mean is calculated by summing all the data points and dividing by the number of data points. The data points are \(9.8, 10.1, 9.8, 10.2, 9.8, 11.1, 11.6\). First, sum them up:
\[

$$\begin{align*} 9.8 + 10.1 + 9.8 + 10.2 + 9.8 + 11.1 + 11.6&=(9.8\times3)+10.1 + 10.2 + 11.1 + 11.6\\ &=29.4+10.1 + 10.2 + 11.1 + 11.6\\ &=29.4 + 10.1=39.5\\ 39.5+10.2&=49.7\\ 49.7+11.1&=60.8\\ 60.8+11.6&=72.4 \end{align*}$$

\]
There are 7 data points, so the mean is \(\frac{72.4}{7}\approx10.34\) (rounded to two decimal places).

Step2: Find the Median

To find the median, first order the data from least to greatest: \(9.8, 9.8, 9.8, 10.1, 10.2, 11.1, 11.6\). Since there are 7 (an odd number) data points, the median is the middle value, which is the 4th value. The 4th value is \(10.1\).

Step3: Find the Mode

The mode is the value that appears most frequently. Looking at the data, \(9.8\) appears 3 times, which is more than any other value. So the mode is \(9.8\).

Answer:

• Mean: \(\approx 10.34\)
• Median: \(10.1\)
• Mode: \(9.8\)