Concept explainers
What’s your favorite TV show? The following table presents the rating for the top 20 prime time shows for the 2007 -2008 season and for the 2012 -2013 season. The rating is the percentage of households with TV sets watched the program
- Find the population standard deviation of the ratings for 2007—2008.
- Find the population standard deviation of the ratings for 2012—2013.
- Compute the
range for the ratings for both seasons. - Based on the standard deviations, did the spread in ratings increase or decrease over the two seasons?
- Based on the ranges, did the spread in ratings increase or decrease over the two seasons?
(a)
To find the population standard deviation for 2007 − 2008.
Answer to Problem 35E
The population standard deviation of the ratings for
Explanation of Solution
Given information:
Top Rated TV programs:
Programs | Rating |
American Idol −− Tuesday | |
American Idol −− Wednesday | |
Dancing With the Star −− Monday |
|
Dancing With the Star −− Tuesday |
|
Dancing With the Star −− Monday |
|
Dancing With the Star −− Tuesday |
|
Desperate Housewives | |
CIS | |
House −− Tuesday | |
Grey’s Anatomy | |
Sunday Night Football | |
CIS: Miami | |
House −− Monday | |
NCIS | |
Survivor: China | |
Without a Trace | |
The Moment of Truth | |
Two and a Half Men | |
|
|
Criminal Minds | |
Top Rated TV Programs: 2012-2013
Programs | Rating |
NBC Sunday Night Football | 7.9 |
Bing Bang Theory | 6.2 |
The Voice | 5.1 |
Modern Family | 4.9 |
The Voice- Tuesday | 4.6 |
American Idol -Wednesday | 4.6 |
American Idol -Thursday | 4.3 |
The Following | 4.3 |
Two and a Half Men | 4.1 |
Grey's Anatomy | 4.1 |
NCIS | 4.0 |
Football Night in American Part 3 | 4.0 |
Revolution | 3.9 |
2 Broke Girls | 3.7 |
How I Met Your Mother | 3.7 |
Family Guy | 3.6 |
Once Upon a Time | 3.6 |
Survivor- Philippines | 3.5 |
X-Factor - Wednesday | 3.5 |
NCIS : LA | 3.4 |
Concept used:
Following steps of TI-83 calculator are used to calculate the population standard deviation.
- Click on STAT > Edit
- Enter the provided data in L1.
- Press STAT > CALC > 1-Var Stats
- Enter L1 by pressing 2nd and 1.
- Press Enter.
Calculation:
Using the above mentioned step of TI-83 calculator, the obtained output is:
Thus, the population standard deviation
(b)
To calculate the population standard deviation for 2012 − 2013.
Answer to Problem 35E
The population standard deviation of the ratings for year
Explanation of Solution
Calculation:
Using the TI-83 calculator, the obtained output is:
Thus, the population standard deviation of the ratings for
(c)
To calculate the range for both years.
Answer to Problem 35E
The range of the ratings for
The range of the ratings for
Explanation of Solution
The range of the set of data is the difference between the largest and smallest values of the data.
The range is calculated as:
The range of the ratings for the year 2007-2008 can be calculated as:
Similarly, the range of the ratings for the year 2012-2013 can be calculated as:
Thus, the range of the ratings for the years 2007-2008 and 2012-2013 are 7.9 and 4.5 respectively.
(d)
To explain whether the spread increases or decrease over the two seasons based on standard deviation.
Answer to Problem 35E
Yes, there is a decrease in spread ove.r the two seasons
Explanation of Solution
The population standard deviation of the ratings for
The population standard deviation of the ratings for
Based on the population standard deviation, the spread in ratings has decreased over the two seasons.
(e)
To explain whether the spread increase or decrease over the two seasons based on the range.
Answer to Problem 35E
Based on the ranges, the spread in ratings decrease over the two seasons
Explanation of Solution
The range of the ratings for
The range of the ratings for
Based on the ranges, the spread in ratings decrease over the two seasons
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