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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=∑χn=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–Min=600–350=$250

Therefore, the range is $250.

04

Estimating the standard deviation

Variance=∑χ−2n−1=400−4652+350−4652+600−4652+525−4652+450−46525−1=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

Consider the horizontal box plot shown below.


a.What is the median of the data set (approximately)?

b.What are the upper and lower quartiles of the data set (approximately)?

c.What is the interquartile range of the data set (approximately)?

d.Is the data set skewed to the left, skewed to the right, or symmetric?

e.What percentage of the measurements in the data set lie to the right of the median? To the left of the upper quartile?

f.Identify any outliers in the data.

Crash tests on new cars.The National Highway Traffic Safety Administration (NHTSA) crash-tests new car models to determine how well they protect the driver and front-seat passenger in a head-on collision. The NHTSA has developed a “star” scoring system for the frontal crash test, with results ranging from one star (*) to five stars (*****). The more stars in the rating, the better the level of crash protection in a head-on collision. The NHTSA crashtest results for 98 cars (in a recent model year) are stored in the accompanying data file.

a. The driver-side star ratings for the 98 cars are summarized in the Minitab printout shown below. Use the information in the printout to form a pie chart. Interpret the graph.

Tally for Discrete Variables: DRIVSTAR

DRIVSTAR

Count

Percent

2

3

4

5

N =

4

17

59

18

98

4.08

17.35

60.20

18.37


b. One quantitative variable recorded by the NHTSA is the driver’s severity of head injury (measured on a scale from 0 to 1,500). The mean and standard deviation for the 98 driver head-injury ratings are displayed in the Minitab printout below. Give a practical interpretation of the mean.
Descriptive Statistics: DRIVHEAD

Variable

N

Mean

StDev

Minimum

Q1

Median

Q3

Maximum

DRIVHEAD

98

603.7

185.4

216.0

475.0

605.0

724.3

1240.0

C. Use the mean and standard deviation to make a statement about where most of the head-injury ratings fall.

d..Find the z-score for a driver head-injury rating of 408. Interpret the result.

Symmetric or skewed?Would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.

a.The salaries of all persons employed by a large university

b.The grades on an easy test

c.The grades on a difficult test

d.The amounts of time students in your class studied last week

e.The ages of automobiles on a used-car lot

f.The amounts of time spent by students on a difficult examination (maximum time is 50 minutes)

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

Ranking driving performance of professional golfers.A group of researchers developed a new method forranking the total driving performance of golfers on theProfessional Golf Association (PGA) tour (The Sport Journal,Winter 2007). The method requires knowinga golfer’s average driving distance (yards) and drivingaccuracy (percent of drives that land in the fairway).The values of these two variables are used to compute adriving performance index. Data for 40 PGA golfers (asranked by the new method for a recent tour year) aresaved in the accompanying file. The first five and last fiveobservations are listed in the table below.

a.Find the mean, median, and mode for the 40 driving performance index values.

b.Interpret each of the measures of central tendency, part a.

c.Use the results, part a,to make a statement about the type of skewness in the distribution of driving performance indexes. Support your statement with a graph.
See all solutions

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