Qmb 5305 - Statistics for Managers

Individual Work One – Week Two

QMB 5305 - Statistics for Managers

Loraine J Jackson

Instructor Robert Miner

April 24, 2016

Individual Work One – Week Two

Page 122, Exercise 29

The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50.

 a. Compute the range and interquartile range.

The range is defined as the difference between the lowest and highest values.  In this data set, the range is 32, the difference between the lowest value of 28 and the highest value of 60. The interquartile range is the difference between the third and first quartiles.

The third quartile is 56.5.

The first quartile is 43.5.

The interquartile range = 56.5 - 43.5 = 13.

b. Compute the sample variance and sample standard deviation.  

The sample variance is 92.7670. The standard deviation is 9.63.

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c. A sample of air quality index readings for Anaheim provided a sample mean of 48.5, a sample variance of 136, and a sample standard deviation of 11.66. What comparisons can you make between the air quality in Pomona and that in Anaheim on the basis of these descriptive statistics?

The mean air quality index reading for Anaheim is higher than Pomona. Also the dispersion in the air quality index readings for Anaheim is higher as compared to Pomona

Page 130, Exercise 44

a. Compute the mean and standard deviation for the points scored by the winning team.

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The mean for this data set is 76.5.  

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The standard deviation for this data set is 7

b. Assume that the points scored by the winning teams for all NCAA games follow a bell-shaped distribution. Using the mean and standard deviation found in part (a), estimate the percentage of all NCAA games in which the winning team scores 84 or more points.

Approximately 68% of the scores are within one standard deviation. Therefore, half of (100–68), or 16%, of the games should have a winning score of 84 or more points.

Estimate the percentage of NCAA games in which the winning team scores more than 90 points.

Approximately 95% of the scores are within two standard deviations. Therefore, half of (100–95), or 2.5%, of the games should have a winning score of more than 90 points.

c. Compute the mean and standard deviation for the winning margin. Do the data contain outliers? Explain.