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Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter1: Introduction To Algebra

Section1.3: Equations

Problem 10MRE

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Question

A man surveyed a sample of 36 high school students and asked, "How many days in the past week have you consumed an alcoholic beverage?" The results of the survey are shown to the right.

1. Is this data discrete or continuous? Draw a histogram of the data and describe its shape. Describe the shape of the distribution.

2. Based on the shape of the histogram, do you expect the mean to be more than, equal to, or less than the median?

Compute the mean and median. What does this tell you?

The mean is

(Type an integer or decimal rounded to two decimal places as needed.)

The median is

(Type an integer or decimal rounded to two decimal places as needed.)

What do the computed mean and median tell you? Fill in the blanks below. (Use a 25% difference as the criterion for a "substantial" difference between the mean and median.)

The prediction was

incorrect

correct

because the mean

is substantially larger than

is substantially smaller than

is greater than

is not equal to

is equal to

is less than

the median in this distribution.

3. Determine the mode.

The mode is

(Type an integer or decimal rounded to two decimal places as needed.

4. Do you believe that the survey suffers from bias? If so, what type and why?

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

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