Chapter 2, Problem 44SE

Approximately 1.5 million high school students take the SAT each year and nearly 80% of the college and universities without open admissions policies use SAT scores in making admission decisions (College Board, March 2009). The current version of the SAT includes three parts: reading comprehension, mathematics, and writing. A perfect combined score for all three parts is 2400. A sample of SAT scores for the combined three-part SAT are as follows:

1. a. Show a frequency distribution and histogram. Begin with the first class starting at 800 and use a class width of 200.
2. b. Comment on the shape of the distribution.
3. c. What other observations can be made about the SAT scores based on the tabular and graphical summaries?

To determine

Construct the frequency distribution and histogram for the data.

Answer to Problem 44SE

The frequency distribution is tabulated below:

Class	Tally	Frequency
800-999	$|$	1
1000-1199	$\left|\right||$	3
1200-1399	$\cancel{\left|\right|\left|\right|}|$	6
1400-1599	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}$	10
1600-1799	$\cancel{\left|\right|\left|\right|}\left|\right|$	7
1800-1999	$\left|\right|$	2
2000-2199	$|$	1
Total		30

• Output using MINITAB software is given below:

Explanation of Solution

Calculation:

The data represents the sample of SAT scores for combined three part sat scores.

The frequencies are calculated by using the tally mark and the method of grouping is used because, range of the data is from 800 to 2,199. Here, the number of times each class levels repeats is the frequency of that particular class.

• From the given data set it is given that the class should be from approximately started with the class of 800 with class width of about 200.
• Make a tally mark for each value in the corresponding class and continue for all values in the data.
• The number of tally marks in each class represents the frequency, f of that class.

Similarly, the frequency of remaining classes for the data set is given below:

Class	Tally	Frequency
800-999	$|$	1
1000-1199	$\left|\right||$	3
1200-1399	$\cancel{\left|\right|\left|\right|}|$	6
1400-1599	$\cancel{\left|\right|\left|\right|}\cancel{\left|\right|\left|\right|}$	10
1600-1799	$\cancel{\left|\right|\left|\right|}\left|\right|$	7
1800-1999	$\left|\right|$	2
2000-2199	$|$	1
Total		30

Software procedure:

Step by step procedure to draw the frequency histogram chart by using MINITAB software.

• Choose Graph > Histogram.
• Choose Simple, and then click OK.
• In Graph variables, enter the corresponding column of data.
• In scale on y-axis, make click on frequency.
• Click on ok.

To determine

Comment the shape of the distribution.

Answer to Problem 44SE

The distribution of sat score is approximately symmetric.

Explanation of Solution

Symmetric distribution:

When the left and right sides of the distribution are approximately equal or mirror images of each other and three distributions will fall under symmetric distribution that is bell shaped, triangular and uniform or rectangular and then it is symmetric distribution.

From the graph, it is observed that the left and right side of the histogram is approximately equal. Hence, the shape of the distribution is bell-shaped curve.

Thus, it can be concluded that the distribution is approximately symmetric.

To determine

Comment the observations of sat scores based on the tabular and graphical summary.

Explanation of Solution

From the data and the histogram, it is observed that approximately 33 percent of sat score (frequency about 10 of 30) will lie between 1400 and 1599.

• Moreover, the score less than 800 or greater than 2,200 are unusual and the average value of sat scores is over 1,500.