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24. A sample of midterm grades for five students showed the following results: 72, 65, 82, 90, 76.

Which of the following statements are correct, and which should be challenged as being too generalized?

a. The average midterm grade for the sample of five students is 77.

b. The average midterm grade for all students who took the exam is 77.

c. An estimate of the average midterm grade for all students who took the exam is 77.

d. More than half of the students who take this exam will score between 70 and 85.

e. If five other students are included in the sample, their grades will be between 65 and 90.

25. Table 18 shows a data set containing information for 25 of the shadow stocks tracked by the American Association of Individual Investors. Shadow stocks are common stocks of smaller companies that are not closely followed by Wall Street analysts. The data set is also on the website that accompanies the text in the file named Shadow(2).

a. How many variables are in the data set?

b. Which of the variables are categorical and which are quantitative?

c. For the Exchange variable, show the frequency and the percent frequency for AMEX, NYSE, and OTC. Construct a bar graph similar to Figure 1.5 for the Exchange variable.

d. Show the frequency distribution for the Gross Profit Margin using the five intervals: 0-14.9, 15–29.9, 30–44.9, 45–59.9, and 60–74.9. Construct a histogram similar to Figure 1.6.

e. What is the average price/earnings ratio?

Answer :


The question is about analyzing a data set including variables for midterm grades, exchanges, and gross profit margin.

The answer provides step-by-step instructions for determining the number of variables in the data set, identifying categorical and quantitative variables, calculating frequency and percent frequency for a categorical variable, constructing a histogram, and calculating the average price-earnings ratio.

Explanation:
a. There are 5 variables in the data set because there are 5 different grades given for the midterm.
b. The variable 'Midterm Grade' is quantitative because it consists of numerical values.
c. The variable 'Exchange' is categorical because it consists of categories such as AMEX, NYSE, and OTC. The frequency and percent frequency for each category can be calculated.
d. To construct a histogram for the 'Gross Profit Margin', calculate the frequency for each interval and then plot the histogram similar to Figure 1.6.
e. The average price-earnings ratio can be calculated by finding the mean of the given data.

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