/*! 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

STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls鈥� participation in informal science, technology, engineering, or mathematics (STEM) programs. The results of the study were published in Cascading Influences: Long-Term Impacts of Informal STEM Experiences for Girls (March 2013). The researchers sampled 174 young women who recently participated in a STEM program. They used a pie chart to describe the geographic location (urban, suburban, or rural) of the STEM programs attended. Of the 174 STEM participants, 107 were in urban areas, 57 in suburban areas, and 10 in rural areas.

a. Determine the proportion of STEM participants from urban areas.

b. Determine the proportion of STEM participants from suburban areas.

c. Determine the proportion of STEM participants from rural areas.

d. Multiply each proportion in parts a鈥攃 by 360 to determine the pie slice size (in degrees) for each location.

e. Use the results, part d, to construct a pie chart for the geographic location of STEM participants.

f. Interpret the pie slice for urban areas.

g. Convert the pie chart into a bar graph. Which, in your opinion, is more informative?

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

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

Construct a relative frequency histogram for the data summarized in the accompanying table.

Sanitation inspection of cruise ships. Refer to the Centres for Disease Control and Prevention listing of the October 2015 sanitation scores for 20 cruise ships, Exercise 2.24 (p. 83).

a. Find the mean and standard deviation of the sanitation scores.

b. Calculate the intervals x {s, x {2s, x {3s.

c. Find the percentage of measurements in the data set that fall within each interval, part

b. Do these percentages agree with Chebyshev鈥檚 Rule? The Empirical Rule?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Geometry

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.