Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

143SE

Expert-verified

Statistics For Business And Economics

Found in: Page 142

Book edition 13th

Author(s) James T. McClave, P. George Benson, Terry Sincich

Pages 888 pages

ISBN 9780134506593

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

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

a. Mean = $465

b. Median = $450

c. Range = $250

d. Standard Deviation = $99.37

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Calculating the mean

x = 400, 350, 600, 525, 450

$\begin{matrix} Mean = \frac{\sum χ}{n} \\ = \frac{400 + 350 + 600 + 525 + 450}{5} \\ = \frac{2325}{5} \\ = $ 465 \end{matrix}$

Therefore, the mean value of books is $465.

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.

Finding the range

Maximum value = $600

Minimum value = $350

$\begin{matrix} Range = Max - Min \\ = 600 - 350 \\ = $ 250 \end{matrix}$

Therefore, the range is $250.

Estimating the standard deviation

$\begin{matrix} Variance = \frac{\sum {(χ -)}^{2}}{n - 1} \\ = \frac{{(400 - 465)}^{2} + {(350 - 465)}^{2} + {(600 - 465)}^{2} + {(525 - 465)}^{2} + {(450 - 465)}^{2}}{5 - 1} \\ = \frac{4225+13225+18225+3600+225}{4} \\ = \frac{39500}{4} \end{matrix}$

$= 9875$

$\begin{matrix} Standard Deviation = \sqrt{Variance} \\ = \sqrt{9875} \\ = 99.37 \end{matrix}$

Therefore, the standard deviation is $99.37.

Most popular questions for Math Textbooks

Salary offers to MBAs. Consider the top salary offer (in thousands of dollars) received by each member of a sample of 50 MBA students who graduated from the Graduate School of Management at Rutgers, the state university of New Jersey. Descriptive statistics and a box plot for the data are shown on the XLSTAT printouts at the top of the next column. [Note: The “+” on the box plot represents the location of the mean.]

a. Find and interpret the z-score associated with the highest salary offer, the lowest salary offer, and the mean salary offer. Would you consider the highest offer to be unusually high? Why or why not?

b. Based on the box plot for this data set, which salary offers (if any) are suspect or highly suspect outliers?

Question: Given a data set with a largest value of 760 and a smallest value of 135, what would you estimate the standard deviation to be? Explain the logic behind the procedure you used to estimate the standard deviation. Suppose the standard deviation is reported to be 25. Is this feasible? Explain

Motivation of athletes. A statistician keeps track of every serve that a player hits during the U.S. Open Tennis Championship. The statistician reports that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph.

a. Suppose the statistician also observes that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player’s serves was between 115 mph and 145 mph?

b. Consider the following serve speeds: 50 mph, 80 mph, and 105 mph. Using the z-score approach for detecting outliers, which of these would represent outliers in the distribution of the player’s serve speeds?

c. If nothing is known about the shape of the distribution, what percentage of the player’s serve speeds are less than 70 mph?

Give the percentage of measurements in a data set that are above and below each of the following percentiles:

a. 75^th percentile

b. 50^th percentile

c. 20^th percentile

d. 84^th percentile

In terms of percentiles, define QL, QM and QU

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free