/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q56E Answer the following questions a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Q56E (page 103)

Answer the following questions about the variability of data sets:

a.What is the primary disadvantage of using the range to compare the variability of data sets?

b.Describe the sample variance using words rather than a formula. Do the same with the population variance.

c.Can the variance of a data set ever be negative? Explain. Can the variance ever be smaller than the standard deviation? Explain.

Short Answer

Expert verified

a) Same range but different data variation

b) Sample variance is the squared summation of the differences in observations from the mean divided by the number of observations minus one. Population variance is the summation of squared differences from the mean divided by the total number of observations.

c) No, the variance can never be negative. Yes, the variance can be smaller than the standard deviation.

Step by step solution

01

Disadvantage of using range to compare data variation

It is not advisable to use range to compare data variation because the range might be the same for two data sets. Still, there might be a very significant difference in the variation of the data.

For example, the range of heights in two groups of students may be the same, but there are chances that the height of students in group 1 is spread out symmetrically, and the height of students in group 2 is concentrated to the right.

02

Describing sample variance and population variance in words.

Sample variance is the squared summation of the differences of observations from the mean divided by the number of observations minus one.

Population variance is the summation of squared differences from the mean divided by the total number of observations.

03

Variance of a data set ever be negative or not

No, the variance cannot be negative because it is the square of deviations from the mean. And based on the basic mathematic rules, a square can never be negative.

The variance can be smaller than the standard deviation when the observations range between 0 and 1.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Question: Color and clarity of diamonds.Diamonds are categorized according to the 鈥渇our C鈥檚鈥�: carats, clarity, color, and cut. Each diamond stone that is sold on the open market is provided a certificate by an independent diamond assessor that lists these characteristics. Data for 308 diamonds were extracted from Singapore鈥檚 Business Times (Journal of Statistics Education, Vol. 9, No. 1, 2001). Color is classified as D, E, F, G, H, or I, while clarity is classified as IF, VVS1, VVS2, VS1, or VS2. In addition to color and clarity, the independent certification group (GIA, HRD, or IGI), the number of carats, and the asking price were recorded.

a.Use a graphical technique to summarize the color and clarity of the 308 diamond stones. What is the color and clarity that occurs most often? Least often?

b.Use a graphical method to describe the carat distribution of all 308 diamonds.

c.Use a graphical method to describe the carat distribution of diamonds certified by the GIA group.

d.Repeat part cfor the HRD and IGI certification groups.

e.Compare the three-carat distributions, parts cand d.Is there one particular certification group that appears to be assessing diamonds with higher carats than the others?

f.Find and interpret the mean of the data set.

g.Find and interpret the median of the data set.

h.Find and interpret the mode of the data set.

i.Which measures of central tendency best describe the 308-carat values? Explain.

j.Use the mean and standard deviation to form an interval that will contain at least 75% of the carat values in the data set.

k.Construct a scatter plot for the data, with a number of carats on the horizontal axis and price on the vertical axis. What type of trend do you detect?

Question:A company is analysing the prices at which its items are sold. Graph the relative frequency histogram for the 600 items summarized in the accompanying relative frequency table.

Compare the z-scores to decide which of the following x values lie the greatest distance above the mean and the greatest distance below the mean.

a.鈥�x=100,鈥�鈥�渭=50,鈥�鈥�蟽=25b.鈥�x=1,鈥�鈥�渭=4,鈥�鈥�蟽=1c.鈥�x=0,鈥�鈥�渭=200,鈥�鈥�蟽=100d.x=10,鈥�鈥�渭=5,鈥�鈥�蟽=3

Thousands of students apply for admission to graduate schools in economics each year with the intention of obtaining a PhD. The Southern Economic Journal (April 2008) published a guide to graduate study in economics by ranking the PhD programs at 129 colleges and universities. Each program was evaluated according to the number of publications published by faculty teaching in the PhD program and by the quality of the publications. Data obtained from the Social Science Citation Index (SSCI) were used to calculate an overall productivity score for each PhD program. The mean and standard deviation of these 129 productivity scores were then used to compute a z-score for each economics program. Harvard University had the highest z-score 1z = 5.082 and, hence, was the top-ranked school; Howard University was ranked last because it had the lowest z-score 1z = -0.812. The data (z-scores) for all 129 economic programs are saved in the data file.

a. Interpret the z-score for Harvard University.

b. Interpret the z-score for Howard University.

c. The authors of the Southern Economic Journal article note that 鈥渙nly 44 of the 129 schools have positive z-scores, indicating that the distribution of overall productivity is skewed to the right.鈥� Do you agree?

Surface roughness of oil field pipe.Oil field pipes are internally coated to prevent corrosion. Researchers at the University of Louisiana, Lafayette, investigated the influence that coating may have on the surface roughness of oil field pipes (Anti-corrosion Methods and Materials, Vol. 50, 2003). A scanning probe instrument was used to measure the surface roughness of each in a sample of 20 sections of coated interior pipe. The data (in micrometers) are provided in the table.

(1.72, 2.50, 2.16, 2.13, 1.06, 2.24, 2.3,1 2.03, 1.09, 1.40, 2.57, 2.64, 1.26, 2.05, 1.19, 2.13, 1.27, 1.51, 2.41, 1.95)

a.Find and interpret the mean of the sample.

b.Find and interpret the median of the sample.

c.Which measure of central tendency鈥攖he mean or the median鈥攂est describes the surface roughness of the sampled pipe sections? Explain.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.