3. Describing Data Numerically

Suppose you have four distributions: A is symmetric and centered at $0$, B is right-skewed with most values above $0$, C is left-skewed with most values below $0$, and D is uniform between $-5$ and $5$. Which of these distributions is likely to have the largest mean?

Given forecast errors of $-1$, $4$, $8$, and $-3$, what is the mean absolute deviation?

Which of the following best describes the $\mathrm{mean}$ in a data set?

You read $105$ pages of a novel over $7$ days. What is the mean number of pages you read each day?

Given a sample with a sample mean of $\overline{x}$ and a sample standard deviation of $s$, which of the following best describes the sample mean?

Which of the following is a good point estimator for the population mean?

Find the mean of the sample data below.

Geometric Mean The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. To find the geometric mean of n values (all of which are positive), first multiply the values, then find the nth root of the product. For a 6-year period, money deposited in annual certificates of deposit had annual interest rates of 0.58%, 0.29%, 0.13%, 0.14%, 0.15%, and 0.19%. Identify the single percentage growth rate that is the same as the six consecutive growth rates by computing the geometric mean of 1.0058, 1.0029, 1.0013, 1.0014, 1.0015, and 1.0019.

Weighted Mean A student of the author earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned grades of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60% of the final grade, the final exam counts for 10%, the project counts for 15%, and homework counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on.

In Exercises 29–32, compute the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (29) 31.4 minutes; (Exercise 30) 140.6 minutes; (Exercise 31) 55.2 years; (Exercise 32) 240.2 seconds.

What’s Wrong? Education Week magazine published a list consisting of the mean teacher salary in each of the 50 states for a recent year. If we add the 50 means and then divide by 50, we get \$56,479. Is the value of \$56,479 the mean teacher salary for the population of all teachers in the 50 United States? Why or why not?

Degrees of Freedom Five recent U.S. presidents had a mean age of 56.2 years at the time of their inauguration. Four of these ages are 64, 46, 54, and 47.

a. Find the missing value.