/*! 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} Problem 29 Can the standard deviation have ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 29

Can the standard deviation have a negative value? Explain.

Short Answer

Expert verified
No, the standard deviation cannot have a negative value. It is calculated as the square root of variance, which cannot be negative.

Step by step solution

01

Understanding standard deviation

Standard deviation is a statistic that measures the dispersion of a dataset relative to its mean. It is calculated as the square root of variance.
02

Variance Calculation

Variance is calculated by taking the mean of the data points, subtracting the mean from each of the data points (differences), squaring each of the differences, calculating the mean of these squared differences, which results in variance.
03

Standard Deviation Calculation

Once the variance is calculated, standard deviation is found by taking the square root of the variance.
04

Analysis of Negative Value

Since variance involves squaring of differences that eliminates any negative signs, it is always non-negative. Consequently, standard deviation, which is the square root of variance, also can never be negative since square root of a positive number or zero is always positive or zero. Hence, a negative standard deviation is not possible.

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

The following data set belongs to a population: \(\begin{array}{llllll}5 & -7 & 2 & 0 & -9 & 16\end{array}\) \(\begin{array}{ll}10 & 7\end{array}\) Calculate the mean, median, and mode.

The following data give the times (in minutes) that all 10 students took to complete an assignment in a statistics class. \(\begin{array}{llllllllll}15 & 26 & 16 & 36 & 31 & 13 & 29 & 18 & 21 & 39\end{array}\) a. Calculate the range, variance, and standard deviation for these data. b. Calculate the coefficient of variation. c. What does the high value of the standard deviation tell you?

The mean age of six persons is 46 years. The ages of five of these six persons are \(57,39,44,51\), and 37 years, respectively. Find the age of the sixth person.

The following data give the annual salaries (in thousand dollars) of 20 randomly selected health care workers. \(\begin{array}{llllllllll}50 & 71 & 57 & 39 & 45 & 64 & 38 & 53 & 35 & 62 \\\ 74 & 40 & 67 & 44 & 77 & 61 & 58 & 55 & 64 & 59\end{array}\) a. Compute the range, variance, and standard deviation for these data. b. Calculate the coefficient of variation. c. Are the values of these summary measures population parameters or sample statistics? Explain.

The following data give the total food expenditures (in dollars) for the past one month for a sample of 20 families. \(\begin{array}{rrrrrrrrrr}1125 & 530 & 1234 & 595 & 427 & 872 & 1480 & 699 & 1274 & 1187 \\ 933 & 1127 & 716 & 1065 & 934 & 1630 & 1046 & 2199 & 1353 & 441\end{array}\) Prepare a box-and-whisker plot. Is the distribution of these data symmetric or skewed? Are there any outliers? If so, classify them as mild or extreme.
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

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.