Chapter 13.2, Problem 15PPS

(a)

To determine

To Draw:TheStem-and-leaf plot of the data.

Answer to Problem 15PPS

  

Explanation of Solution

Given:In the problem you will use the stem-and-leaf plot to analyze the data. The test scores $36$ students are shown in the table at right.

  

Display the data in stem-and-leaf plot.

The stem-and-leaf plot of the data is shown below:

  

(b)

To determine

To Find: The mean, median, and mode of the data.

Answer to Problem 15PPS

Mean= $55.64$

Median= $60.5$

The mode of the data is 59 and $78$

Explanation of Solution

Given: In the problem you will use the stem-and-leaf plot to analyze the data. The test scores $36$ students are shown in the table at right.

  

Finding Mean:

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{6+13+\mathrm{19.....}+80}{36}\\ Mean=\frac{2003}{36}=55.64\end{array}$

Mean= $55.64$

Finding Median:

The number of observations is even

Then

Median

  $median=\frac{59+62}{2}=60.5$

Median= $60.5$

Finding Mode:

The mode of the data is 59 and $78$ as it is most repeating values.

(c)

To determine

To Draw: The graph from Stem-and-leaf plot of the data.

Answer to Problem 15PPS

  

Explanation of Solution

Given: In the problem you will use the stem-and-leaf plot to analyze the data. The test scores $36$ students are shown in the table at right.

  

Turn the stem-and-leaf plot to ${90}^{°}$ counterclockwise. Sketch the graph that is formed by peak of the stem-and-leaf plot.

The graph of the stem-and-leaf plot of the data is shown below:

  

(d)

To determine

To Describe: The data of the number of peaks in the graph.

Answer to Problem 15PPS

The graph is not symmetric

The graph has the two peaks that are marked at the range of $30-40$ and $70-80$ .

Explanation of Solution

Given: In the problem you will use the stem-and-leaf plot to analyze the data. The test scores $36$ students are shown in the table at right.

  

Describe the data by the number of peaks in the graph. Is it symmetric? Explain.

The graph has the two peaks that are marked at the range of $30-40$ and $70-80$ .

The graph is not symmetric

(e)

To determine

To Describe: The data is skewed or not.

Answer to Problem 15PPS

The data set is skewed

Explanation of Solution

Given: In the problem you will use the stem-and-leaf plot to analyze the data. The test scores $36$ students are shown in the table at right.

  

A set of data can be described as being skewed if the graph of the data is not symmetric. Is the data is skewed? Explain.

Since the data is not symmetric

The data set is skewed.