3. Describing Data Numerically

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

Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.

Grades A student receives the grades shown below, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student’s grade point average?

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

Grade-Point Average Marissa has just completed her second semester in college. She earned a B in her five-hour calculus course, an A in her three-hour social work course, an A in her four-hour biology course, and a C in her three-hour American literature course. Assuming that an A equals 4 points, a B equals 3 points, and a C equals 2 points, determine Marissa’s grade-point average for the semester.

In Exercises 5–8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

What is the value of x_double bar In general, how is a value of xbar found?

[NW] [DATA] TelevisionsIn the Sullivan Statistics Survey I, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.

c. Calculate and explain the mean of the random variable X.

Body Temperatures Listed below are body temperatures (°F) of adult males (based on Data Set 5 “Body Temperatures” in Appendix B).

97.6 98.2 99.6 98.7 99.4 98.2 98.0 98.6 98.6

a. Find the mean. Does the result seem reasonable?

Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.

Populations The populations (in thousands) of the counties in Montana in 2019 (Source: U.S. Census Bureau)

"Kiosks Yolanda opened a new fast food restaurant. From her first customer, Yolanda kept track of the time a patron needed to wait from the time placing the order to the time the customer received his/her order. Because she was unhappy with the wait time, she invested in Kiosks to take orders with the goal of decreasing wait times. In a random sample of 20 customers, it was found the wait time was 52.3 seconds.

b. Determine the mean wait time of the 10,303 customers."

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?

Trimmed Mean Because the mean is very sensitive to extreme values, we say that it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and delete the top 10% of the values, then calculate the mean of the remaining values. Use the axial loads (pounds) of aluminum cans listed below (from Data Set 41 “Aluminum Cans” in Appendix B) for cans that are 0.0111 in. thick. An axial load is the force at which the top of a can collapses. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean.

247 260 268 273 276 279 281 283 284 285 286 288

289 291 293 295 296 299 310 504

Quadratic Mean The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of that result, as indicated below:

Quadratic mean = sqrt(∑x^2/n)

Find the R.M.S. of these voltages measured from household current: 0, 60, 110, 0. How does the result compare to the mean?

Find the mean of the sample data below.