Concept explainers
a.
To calculate: The mean, median, and standard deviation for the temperatures in Los Angeles.
a.
Answer to Problem 8CFU
The mean , median , and standard deviation for the temperatures in Los Angeles are
Explanation of Solution
Given information:
The normal maximum daily temperature for Los Angeles.
Los Angeles | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
65.7 | 65.9 | 65.5 | 67.4 | 69.0 | 71.9 | 75.3 | 76.6 | 76.6 | 74.4 | 70.3 | 65.9 |
Formula used:
Formula of Mean
Median for even terms =
Median for odd terms =
A measure of variability associated with the arithmetic mean is the standard deviation.
Calculation:
Consider the data in ascending order ,
So,
The mean of the data is
There is even number of data.
The median of even number of data is −
The standard deviation is −
65.5 | 70.375 | ||
65.7 | 70.375 | ||
65.9 | 70.375 | ||
65.9 | 70.375 | ||
67.4 | 70.375 | ||
69.0 | 70.375 | ||
70.3 | 70.375 | ||
71.9 | 70.375 | ||
74.4 | 70.375 | ||
75.3 | 70.375 | ||
76.6 | 70.375 | ||
76.6 | 70.375 | ||
Hence, the mean , median , and standard deviation for the temperatures in Los Angeles are
b.
To calculate: The mean, median, and standard deviation for the temperatures in Las Vegas.
b.
Answer to Problem 8CFU
The mean , median , and standard deviation for the temperatures in Los Angeles are
Explanation of Solution
Given information:
The normal maximum daily temperature for Las Vegas .
Las Vegas | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
57.3 | 63.3 | 68.8 | 77.5 | 87.8 | 100.3 | 105.9 | 103.2 | 94.7 | 82.1 | 67.4 | 57.5 |
Formula used:
Formula of Mean
Median for even terms =
Median for odd terms =
A measure of variability associated with the arithmetic mean is the standard deviation.
Calculation:
Consider the data in ascending order,
So,
The mean of the data is
There is even number of data.
The median of even number of data is −
The standard deviation is −
57.3 | 80.48 | ||
57.5 | 80.48 | ||
63.3 | 80.48 | ||
67.4 | 80.48 | ||
68.8 | 80.48 | ||
77.5 | 80.48 | ||
82.1 | 80.48 | ||
87.8 | 80.48 | ||
94.7 | 80.48 | ||
100.3 | 80.48 | ||
103.2 | 80.48 | ||
105.9 | 80.48 | ||
Hence, the mean , median , and standard deviation for the temperatures in Los Angeles are
c.
To sketch : The box-and-whisker plot for the temperatures for each city.
c.
Explanation of Solution
Given information:
The normal maximum daily temperature for Los Angeles and Las Vegas.
Los Angeles | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
65.7 | 65.9 | 65.5 | 67.4 | 69.0 | 71.9 | 75.3 | 76.6 | 76.6 | 74.4 | 70.3 | 65.9 | |
Las Vegas | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
57.3 | 63.3 | 68.8 | 77.5 | 87.8 | 100.3 | 105.9 | 103.2 | 94.7 | 82.1 | 67.4 | 57.5 |
Graph:
Figure1.
Figure2.
Interpretation:
The figure1 and figure 2 represent the temperature of the Los Angeles and Las Vegas respectively.
d.
To show: Which of the city has a smaller variability in temperature.
d.
Answer to Problem 8CFU
Las Vegas has a smaller variability in temperature.
Explanation of Solution
Given information:
The normal maximum daily temperature for Los Angeles and Las Vegas.
Los Angeles | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
65.7 | 65.9 | 65.5 | 67.4 | 69.0 | 71.9 | 75.3 | 76.6 | 76.6 | 74.4 | 70.3 | 65.9 | |
Las Vegas | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
57.3 | 63.3 | 68.8 | 77.5 | 87.8 | 100.3 | 105.9 | 103.2 | 94.7 | 82.1 | 67.4 | 57.5 |
Calculation:
Record of Los Angeles
Terms | 12 |
Mean | 80.48 |
Median | 79.8 |
Standard Deviation | 17.0551 |
Record of Las Vegas
Terms | 12 |
Mean | 70.375 |
Median | 69.65 |
Standard Deviation | 3.1352 |
Observing the record , Las Vegas has a smaller variability in temperature. As each measure of Las Vegas is lesser than the Los Angeles.
e.
To show: The cause one city might have a greater variability in temperature than another.
e.
Answer to Problem 8CFU
Pollution, temperature and many more.
Explanation of Solution
Given information:
The normal maximum daily temperature for Los Angeles and Las Vegas.
Los Angeles | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
65.7 | 65.9 | 65.5 | 67.4 | 69.0 | 71.9 | 75.3 | 76.6 | 76.6 | 74.4 | 70.3 | 65.9 | |
Las Vegas | Jan | Feb | March | April | May | June | July | August | Sept | Oct | Nov | Dec |
57.3 | 63.3 | 68.8 | 77.5 | 87.8 | 100.3 | 105.9 | 103.2 | 94.7 | 82.1 | 67.4 | 57.5 |
Calculation:
Record of Los Angeles
Terms | 12 |
Mean | 80.48 |
Median | 79.8 |
Standard Deviation | 17.0551 |
Record of Las Vegas
Terms | 12 |
Mean | 70.375 |
Median | 69.65 |
Standard Deviation | 3.1352 |
The reason might the pollution, humidity, environment and could affect the temperature of the cities in large variation.
Chapter 14 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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Basic Business Statistics, Student Value Edition
University Calculus: Early Transcendentals (4th Edition)
Thinking Mathematically (6th Edition)
Algebra and Trigonometry (6th Edition)
A First Course in Probability (10th Edition)
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