Chapter 2, Problem 44SE

Approximately 1.5 million high school students take the SAT each year and nearly 80% of colleges and universities without open admissions policies use SAT scores in making admission decisions. 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 is as follows.

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

To determine

(a)

To Check:

Show a frequency distribution and histogram.

Answer to Problem 44SE

Class	Frequency	Frequency distribution
800-1000	1	1/30 =0.033
1000-1200	2	2/30 = 0.066
1200-1400	6	6/30 =0.2
1400-1600	9	9/30= 0.3
1600-1800	8	8/30= 0.266
1800-2000	3	3/30= 0.1
2000-2200	1	1/30=0.033

  

Explanation of Solution

Let's make a table with a class width of 200 to show frequency distribution.

Frequency distribution can be calculated as

Frequency distribution of a class = Number of values falling in that class/ total number of values in the data set.

class	frequency	Frequency distribution
800-1000	1	1/30 =0.033
1000-1200	2	2/30 = 0.066
1200-1400	6	6/30 =0.2
1400-1600	9	9/30= 0.3
1600-1800	8	8/30= 0.266
1800-2000	3	3/30= 0.1
2000-2200	1	1/30=0.033

  

To determine

(b)

To Check:

Comment on the shape of the distribution

Answer to Problem 44SE

While looking at the histogram we can see that the distribution is roughly Normal distribution but is right skewed.

Explanation of Solution

While looking at the histogram we can see that the distribution is roughly Normal distribution but is right skewed.

To determine

(c)

To Check:

What other observations can be made from graph and table

Answer to Problem 44SE

SAT score between1400 − 1600 is most frequent. None of the students scored above 2200

Explanation of Solution

After looking at the table and the histogram we can see that SAT score between1400 − 1600 is most frequent. None of the students scored above 2200