Concept explainers
(a)
To identify the shape of each distribution.
(a)
Answer to Problem 21E
Both the brands are skewed right.
Explanation of Solution
Given information: Box-and-whisker plot.
Calculation:
Both the brands are skewed right.
Fewer data plots are found to the right of the graph. The "tail" of the graph is pulled toward higher positive numbers, or to the right. The mean typically gets pulled toward the tail, and is greater than the median.
(b)
To find the range of upper
(b)
Answer to Problem 21E
Range of upper
Range of upper
Explanation of Solution
Given information: Box-and-whisker plot.
Formula Used:Range of the data=
Calculation:
As the range of the data:
- Brand A
Range of upper
So,
Range of upper
Hence,
Range of upper
- Brand B
Range of upper
So,
Range of upper
Hence,
Range of upper
(c)
To find the interquartile range of data.
(c)
Answer to Problem 21E
InterquartileRange of brand A=
InterquartileRange of brand B=
Explanation of Solution
Given information: Box-and-whisker plot.
Formula Used:InterquartileRange of the data=
Calculation:
As the range of the data:
- Brand A
InterquartileRange of brand A=
So,
InterquartileRange of brand A=
Hence,
InterquartileRange of brand A=
- Brand B
InterquartileRange of brand B=
So,
InterquartileRange of brand B=
Hence,
InterquartileRange of brand B=
(d)
To find the greater standard deviation.
(d)
Answer to Problem 21E
Brand A has greater standard deviation
Explanation of Solution
Given information: Box-and-whisker plot.
Formula Used:Standard deviation =
Calculation:
The standard deviation is approximately equal to the
Also,
The standard deviation is approximately equal to
Both estimates work best for normal distribution, i.e. distributions that are not skewed, and the first approximation works best if they are no outliers. They will later determine additional relations between the standard deviation for
Outliers are data points that fall below
- Range A:
Range of brand A=
Now,
Range of brand A=
So,
Standard deviation =
Hence,
Standard deviation of brand A=
- Range B:
Range of brand B =
Now,
Range of brand B =
So,
Standard deviation =
Hence,
Standard deviation of brand B =
(e)
To identify the brand with more battery life.
(e)
Answer to Problem 21E
Brand A
Explanation of Solution
Given information: Box-and-whisker plot.
Calculation:
Range of brand A=
and
Range of brand B =
Hence,
Brand A will be choose because it has greater range than brand B.
Chapter 11 Solutions
BIG IDEAS MATH Integrated Math 1: Student Edition 2016
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