Chapter SH, Problem 11.5EP

a.

To determine

To create a histogram using graphing calculator and then describe the distribution of the shape.

Explanation of Solution

Given:

Consider the SAT Scores of a class:

  

Calculation:

Use TI-83 calculator to create a Histogram for the above data set. The procedure is given as below:

Step 1: Press $STAT$ and press $1$ to select $EDIT$ for entering the data. The screenshot is given as below:

  

Step 2: Enter all the values in L1 one by one, the screenshot is given as below:

  

Step 3: Press $2nd$

  $\text{Y=}$ to select the STAT PLOT, The screenshot is given as below:

  

Step 4: Select the plot number by pressing and then select the histogram plot type as show bellow by pressing. The screenshot is given as below:

  

Step 5: Press $GRAPH$ to visualize the histogram plot. If it’s not displayer properly then press $ZOOM/9$ to get a clear display. The screenshot is given as below:

  

This is the required histogram. From the histogram it’s obvious that the majority of the data are on the left side of the mean hence the data is a Positively Skewed.

b.

To determine

To display the five number summary.

Explanation of Solution

The distributions are skewed therefore use five number summaries to understand the behavior of the data. Calculate the five point summary using TI83 calculator. The procedure is given as below:

Step 1: Press $STAT$ and select CALC.

  

Step 2: Press 1 and $ENTER$ to calculate 1-var statistics. The screenshot of the obtained 1-var statistics is given as below:

  

Step 3: Scroll down to view the five point summary. The screenshot is given as below:

  

Therefore SAT score are range from $1230$ to $2400$ . The median age is $1600$ and the half of the SAT score are lies between $1390$ to $1960$ .