3. Describing Data Numerically

What makes the range less desirable than the standard deviation as a measure of dispersion?

z Scores. In Exercises 5–8, express all z scores with two decimal places.

New York City Commute Time New York City commute times (minutes) are listed in Data Set 31 “Commute Times” in Appendix B. The 1000 times have a mean of 42.6 minutes and a standard deviation of 26.2 minutes. Consider the commute time of 95.0 minutes.

c. Convert the commute time of 95.0 minutes to a z score.

Triathlon Roberto finishes a triathlon (750-meter swim, 5-kilometer run, and 20-kilometer bicycle) in 63.2 minutes. Among all men in the race, the mean finishing time was 69.4 minutes with a standard deviation of 8.9 minutes. Zandra finishes the same triathlon in 79.3 minutes. Among all women in the race, the mean finishing time was 84.7 minutes with a standard deviation of 7.4 minutes. Who did better in relation to their gender?

If a set of data has a standard deviation of $0$, which of the following must be true about the data?

If an observation has a z-score of $0$, which of the following is true?

Comparing Variation in Different Data Sets In Exercises 45–50, find the coefficient of variation for each of the two data sets. Then compare the results.

Heights and Weights The heights (in inches) and weights (in pounds) of every France national soccer team player that started the 2018 FIFA Men’s World Cup final are listed. (Source: ESPN)

In a normal distribution, which of the following statements is true regarding the $\mathrm{mean}$ and the $\mathrm{median}$?

In Problems 5–10, by hand, find the population variance and standard deviation or the sample variance and standard deviation as indicated.

Population: 1, 19, 25, 15, 12, 16, 28, 13, 6

In Exercises 21–28, use the same list of cell phone radiation levels given for Exercises 17–20. Find the indicated percentile or quartile.

Q3

Household Winter Temperature Often, frequency distributions are reported using unequal class widths because the frequencies of some groups would otherwise be small or very large. Consider the following data, which represent the daytime household temperature the thermostat is set to when someone is home for a random sample of 750 households. Determine the class midpoint, if necessary, for each class and approximate the mean and standard deviation temperature.

pH in Water The acidity or alkalinity of a solution is measured using pH. A pH less than 7 is acidic, while a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water. b. Which type of water has more dispersion in pH using the standard deviation as the measure of dispersion?

Why Divide by ? Let a population consist of the values 9 cigarettes, 10 cigarettes, and 20 cigarettes smoked in a day (based on data from the California Health Interview Survey). Assume that samples of two values are randomly selected with replacement from this population. (That is, a selected value is replaced before the second selection is made.)

d. Which approach results in values that are better estimates of part (b) or part (c)? Why? When computing variances of samples, should you use division by n or

Interpreting the Coefficient of Determination

In Exercises 5–8, use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables.

Times of Taxi Rides and Fares r = 0.953 (x = time in minutes, y = fare in dollars)

$Which\; characteristic\; of\; data\; is\; a\; measure\; of\; the\; amount\; that\; the\; data\; values\; vary?$