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Chapter 2: 143SE (page 142)

The amount spent on textbooks for the fall term was recorded for a sample of five university students. The following data were observed: \(400, \)350, \(600, \)525, and $450. Calculate each of the following values for this data:

a.The sample mean

b.The sample median

c.The sample range

d.The standard deviation

Short Answer

Expert verified

a. Mean = $465

b. Median = $450

c. Range = $250

d. Standard Deviation = $99.37

Step by step solution

01

Calculating the mean

x =400, 350, 600, 525, 450

Mean=鈭�蠂n=400+350+600+525+4505=23255=$465

Therefore, the mean value of books is $465.

02

Computing the median

Arranging the data in ascending order,

350, 400, 450, 525, 600

As the sample size is odd, the central value is 450. Therefore, $450 is the median.

03

Finding the range

Maximum value = $600

Minimum value = $350

Range=Max鈥�Min=600鈥�350=$250

Therefore, the range is $250.

04

Estimating the standard deviation

Variance=鈭�蠂鈭�2n鈭�1=400鈭�4652+350鈭�4652+600鈭�4652+525鈭�4652+450鈭�46525鈭�1=4225+13225+18225+3600+2254=395004

=9875

StandardDeviation=Variance=9875=99.37

Therefore, the standard deviation is $99.37.

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Most popular questions from this chapter

Construct a scattergram for the data in the following table.

Variable 1: 174 268 345 119 400 520 190 448 307 252

Variable 2: 8 10 15 7 22 31 15 20 11 9

Improving SAT scores.The National Education Longitudinal Survey (NELS) tracks a nationally representative sample of U.S. students from eighth grade through high school and college. Research published in Chance (Winter 2001) examined the Standardized Assessment Test (SAT) scores of 265 NELS students who paid a private tutor to help them improve their scores. The table summarizes the changes in both the 厂础罢鈥揗补迟丑ematics and 厂础罢鈥揤别谤产补濒 scores for these students.

厂础罢鈥揗补迟丑

厂础罢鈥揤别谤产补濒

Mean change in score

19

7

Standard deviation of score changes

65

49

a.Suppose one of the 265 students who paid a private tutor is selected at random. Give an interval that is likely to contain this student鈥檚 change in the 厂础罢鈥揗补迟丑 score.

b.Repeat part afor the 厂础罢鈥揤别谤产补濒 score.

c.Suppose the selected student increased his score on one of the SAT tests by 140 points. Which test, the SAT鈥� Math or 厂础罢鈥揤别谤产补濒, is the one most likely to have the 140-point increase? Explain.

Compute xbar, s2, and sfor each of the following data sets. If appropriate, specify the units in which your answer is expressed.

a.3, 1, 10, 10, 4

b.8 feet, 10 feet, 32 feet, 5 feet

c.-1, -4, -3, 1, -4, -4

d.1/5 ounce, 1/5 ounce, 1/5 ounce, 2/5 ounce, 1/5 ounce, 4/5 ounce

Question: State SAT scores.Refer to Exercise 2.27 (p. 84) and the data on state SAT scores. Construct a scatterplot for the data, with the 2010 Math SAT score on the horizontal axis and the 2014 Math SAT score on the vertical axis. What type of trend do you detect?

State

2010 Math SAT

2014 Math SAT

Alabama

538

550

Alaska

503

513

Arizona

527

524

Arkansa

571

564

California

510

516

Wisconsin

608

603

Wyoming

599

565

Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.
See all solutions

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