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Chapter 2: Q. 5 (page 137)

What the mean means The figure below is a density curve. Trace the curve onto your paper.

(a) Mark the approximate location of the median. Justify your choice of location.

(b) Mark the approximate location of the mean. Justify your choice of location.

Use the 68-95-99.7 rule to estimate the percent of observations from a Normal distribution that fall in an interval involving points one, two, or three standard deviations on either side of the mean.

Short Answer

Expert verified

a. The median will be significantly to the right of the peak since it will be greater as the most common values grow..

b. Because the median is not affected by extremely large values as effectively as the mean, the mean also lies to the right of the median.

Step by step solution

01

Part(a) Step 1: Concept Introduction

To get the mean of a data set, divide by the number of values in it. The median is the point where the highest and lowest values meet.

02

Part(a) Step 2: Explanation

Because the tail of large values causes the median to grow as the most common values grow, the median will lie slightly to the right of the peak:

03

Part(b) Step 1: Concept Introduction

To get the mean of a data set, divide by the number of values in it. The median is the point where the highest and lowest values meet.

04

Part(b) Step 2: Explanation

Because the tail of large values causes the mean to become larger as the most common values, the mean will lie to the right of the peak.

Because the mean is influenced more strongly by extremely big numbers than the median, it is also to the right of the median.

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Potato chips The distribution of weights of 9-ounce bags of a particular brand of potato chips is approximately Normal with a mean 渭=9.12ounces and standard deviation 伪=0.05ounce. Draw an accurate sketch of the distribution of potato chip bag weights. Be sure to label the mean, as well as the points one, two, and three standard deviations away from the mean on the horizontal axis. Use rule68-95-99.7.

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(b) C and F
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If every observation in a data set is multiplied by 10, the only one of the following that is not multiplied by 10 is

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