Q.87 Given the following box plot, an... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 2: Q.87 (page 148)

Given the following box plot, answer the questions
a. Think of an example (in words) where the data might fit into the above box plot. In 2鈥�5 sentences, write down the example.
b. What does it mean to have the first and second quartiles so close together, while the second to third quartiles are far apart?

Short Answer

Expert verified

a) A survey was conducted by a market research firm to determine how many hours people watch television in a month. The box plot depicts the number of hours per month that panellists spend watching television.

b) Because the data in this quarter is so similar, the first and second quartiles are very close. There isn't a lot of variety in the numbers. The third-quarter data is far more erratic, or spread out. Because the second quartile is so far away from the third quartile, this is obvious.

Step by step solution

Part (a) - Step 1: To think

Of an example where the data might fit into the given box plot.

Part (a) - Step 2: Explanation

Box plots are a graphical tool used in statistics to show the concentration of data. They also demonstrate how far the extreme numbers differ from the majority of the data. The smallest value, the first quartile, the median, the third quartile, and the maximum value are used to create a box plot. These values are used to see how similar other data values are to them.

A box plot can be used to determine how skewed the data is. If the median is roughly in the middle of the box, the data is symmetric. The data is rightskewed if the longer part of the box is to the right of the median. The data is left-skewed if the longer part of the box is to the left of the median.

Now we can imagine that Market Research Company ran a survey to determine how many hours people watch TV in a month for a specific box plot. The box plot depicts the number of hours per month that panellists spend watching television.

Part (b) - Step 3: To determine

What does it mean to have the first and second quartiles so close together, while the third quartiles are far apart?

Part (b) - Step 4: Explanation

The first and second quartiles are visibly close together in the box plot because the data in this quarter is extremely comparable. There isn't a lot of variety in the numbers. The third-quarter data is far more erratic, or spread out. Because the second quartile is so far away from the third quartile, this is obvious.