/*! 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} Q. 3.156 Which measure of variation is pr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q. 3.156 (page 136)

Which measure of variation is preferred when

(a) the mean is used as a measure of center?

(b) the median is used as a measure of center?

Short Answer

Expert verified

(a) The standard deviation is used as a measure of variation.

(b) The interquartile range is used as a measure of variation.

Step by step solution

01

Part (a) Step 1: Given Information

We have to find out the measure of variation when mean is used as a measure of center.

02

Part (a) Step 2: Explanation 

When the mean is taken as a measure of center then we use standard deviation as a measure of variation because it is defined as to move one standard unit away from the mean in either directions.

03

Part (b) Step 1: Given Information

We have to find out the measure of variation when median is used as a measure of center.

04

Part (b) Step 2: Explanation

When median is taken as the measure of center then we use interquartile range as the measure of variation because it is defined using median only and it is the difference between the first quartile and third quartile and it also tells the position of median in the boxplot.

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

Consider the following sample of exam scores, arranged in increasing order.

The sample mean and sample standard deviation of these exam scores are 85and 16.1, respectively.
a. Compare the percentage of the observations that actually lie within two standard deviations to either side of the mean with that given by Chebyshev's rule withk=2
b. Repeat part (a) with k=3
c. Interpret your results from parts (a) and (b).

Fill in the blanks: Roughly, when arranged in increasing order, the uppermost 25%of the dataset are greater than or equal to _______ .

Gestation Periods of Humans. Gestation periods of humans have a mean of 266days and a standard deviation of 16days. Let ydenote the variable "gestation period" for humans.

a. Find the standardized variable corresponding toy

b. What are the mean and standard deviation of the standardized variable?

c. Obtain the z-scores for gestation periods of 227days and 315days. Round your answers to two decimal places.

d. Interpret your answers in part (c).

c. Construct a graph similar to Fig. 3.20 on page 146 that shows your results from parts (b) and (c).

Sickle Cell Disease. A study published by E. Anionwu et al. in the British Medical Journal (Vol. 282, pp. 283-286) examined the steady-state hemoglobin levels of patients with three different types of sickle cell disease: HB SC. HB SS. and HB ST. Use the following boxplots to compare the hemoglobin levels for the three groups of patients, paying special attention to center and variation.

True of False: The mean, median and mode can all be used with quantitative data. Explain your answer.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

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.