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# Analyzing Descriptive Statistics and Graphs

1. The national average of women's times in the 1 mile run is 7.5 minutes with a standard deviation of 1.2 minutes. The male national average is 6.75 minutes with a standard deviation of 0.8 minutes. Your Aunt and Uncle decide to race the mile. His time is 8.35 minutes while
hers is 9.3 minutes. Using the concept of z-scores (z-values), who is the relatively faster runner? Show and explain why.

2. What is the mathematical relationship between standard deviation and variance? Why does it make sense to use the standard deviation (more so than the variance) when discussing real - life data?...for example, dollars, feet, seconds, cars, etc.

3. A multiple choice test (binomial distribution) has 10 questions. Each question has four possible choices. A student guesses the correct answer for each question. Find the probability that the student passes the test if passing is considered to be 6 or more correct.

4. Plywood, Inc. reported these returns on stockholder equity for the past 5 years: 4.3, 4.9, 7.2, 6.7, and 11.6. Consider these as population values.
a. Compute the range, the arithmetic mean, the variance, and the standard deviation.

5. The annual incomes of the five vice presidents of TMV Industries are: \$125,000; \$128,000;
\$122,000; \$133,000; and \$140,000. Consider this a population.
a. What is the range?
b. What is the arithmetic mean income?
c. What is the population variance? The standard deviation?
d. The annual incomes of officers of another firm similar to TMV Industries were also studied.
The mean was \$129,000 and the standard deviation \$8,612. Compare the means
and dispersions in the two firms.

CALCULATING THE STATISTICS

6. Construct a histogram, a frequency polygon, and an ogive for the following frequency distribution.
Class Interval Frequency
50-under 60 13
60-under 70 27
70-under 80 43
80-under 90 31
90-under 100 9

7. Construct a stem and leaf plot for the following data.Let the leaf contain one digit.
312 324 289 335 298
314 309 294 326 317
290 311 317 301 316
306 286 308 284 324

8. An examination of rejects shows at least 10 problems. A frequency tally of the problems follows. Construct a Pareto chart for these data.
Problem Frequency
1 673
2 29
3 108
4 379
5 73
6 564
7 12
8 402
9 54
10 202

9. The top music genres according to SoundScan for a recent year are R&B,Alternative (Rock) Music, Rap, and Country. These and other music genres along with the number of albums sold in each (in millions) are shown.
Genre Albums Sold
R&B 146.4
Alternative 102.6
Rap 73.7
Country 64.5
Soundtrack 56.4
Metal 26.6
Classical 14.8
Latin 14.5

Construct a pie chart for these data displaying the percentage of the whole that each of these genres represents.

#### Solution Summary

The solution gives various descriptive statistics like mean, median and standard deviation. Pareto chart, stem and leaf plot and pie chart are also given for some problems.

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