In 2017 a pollution index was calculated for a sample of cities in the western states using data on air and water pollution. Assume the distribution of pollution indices is unimodal and symmetric. The mean of the distribution was 43.0 points with a standard deviation of 11.3 points.

a. What percentage of western cities would you expect to have a pollution index between 31.7 and 54.3 points?

b. What percentage of western cities would you expect to have a pollution index between 20.4 and 65.6?

c. The pollution index for San Jose in 2017 was 51.9 points. Based on this distribution, was this unusually high? Explain.

Which of these is an advantage to life on land for plants? A) more direct sunlight B) less carbon dioxide C) greater space to grow D) less competition for food

In the most recent summer Olympics, do you think the standard deviation of the running times for all men who ran the 100-meter race would be larger or smaller than the standard deviation of the running times for the men’s marathon? Explain.

The mean birth length for U.S. children born at full term (after 40 weeks) is 52.2 centimeters (about 20.6 inches). Suppose the standard deviation is 2.5 centimeters and the distributions are unimodal and symmetric.

a. What is the range of birth lengths (in centimeters) of U.S.-born children from one standard deviation below the mean to one standard deviation above the mean?

b. Is a birth length of 54 centimeters more than one standard deviation above the mean?

The table show the gold medal Olympic times (in seconds) for the 200-meter run. Data are shown for the first five Olympics of the 1900s and five more recent Olympics in the 2000s.

a. Find and interpret (report in context) the mean and standard deviation of the winning times for the first five Olympics of the 1900s. Round to the nearest hundredth of a second.

b. Find the mean and standard deviation of the winning times for the more recent Olympics.

c. Compare the winning times of the early 1900s and the 2000s Olympics. Are recent winners faster or slower than those of the early 1900s? Which group has less variation in its winning times?

Assume that men’s heights have a distribution that is symmetric and unimodal, with a mean of 69 inches and a standard deviation of 3 inches.

a. What men’s height corresponds to a z-score of 2.00?

b. What men’s height corresponds to a z-score of -1.50?

The top ten movies based on Marvel comic book characters for the U.S. box office as of fall 2017 are shown in the following table, with domestic gross rounded to the nearest hundred million.

a. Sort the domestic gross income from smallest to largest. Find the median by averaging the two middle numbers. Interpret the median in context.

b. Using the sorted data, find Q1 and Q3. Then find the interquartile range and interpret it in context.

c. Find the range of the data. Explain why the IQR is preferred over the range as a measure of variability.

The prices (in $thousand) of a sample of three-bedroom homes for sale in Florida and Georgia are shown in the table.

a. In which state are homes typically more expensive? Support your answer using an appropriate statistic.

b. Which state has more variation in home prices? Support your answer using an appropriate statistic.

c. Notice that one home price in the Florida data ($432.4 thousand) seems a unusually high when compared with the other home prices. What would happen to the standard deviation if this home price was removed from the data? Calculate the standard deviation, omitting this value from the data. Was your prediction correct?

Babies born after 40 weeks gestation have a mean length of 52.2 centimeters (about 20.6 inches). Babies born one month early have a mean length of 47.4 centimeters. Assume both standard deviations are 2.5 centimeters and the distributions are unimodal and symmetric.

a. Find the standardized score (z-score), relative to all U.S. births, for a baby with a birth length of 45 centimeters.

b. Find the standardized score of a birth length of 45 centimeters for babies born one month early, using 47.4 as the mean.

c. For which group is a birth length of 45 centimeters more common? Explain what that means.

Can the sample standard deviation be equal to zero? If so, give an example.

StatCrunch did a survey asking respondents their gender and how much they thought should be spent on a wedding. The following table shows Minitab descriptive statistics for wedding costs, split by gender.

a. How many people were surveyed?

b. Compare the results for men and women. Which group thought more should be spent on a wedding? Which group had more variation in their responses?

Descriptive Statistics: Amount

Statistics

Is it possible for a standard deviation to be equal to zero? Explain.

The table shows the 100-meter backstroke and the 100-meter butterfly gold medal Olympic times (in seconds) for five recent Olympics.

a. Find and interpret (report in context) the mean and standard deviation of the gold medal times for each stroke. Round to the nearest hundredth of a second.

b. Compare the mean and the standard deviation for the two strokes. Which stoke tends to have a faster gold medal time? Which has more variation in winning times?

Suppose a group of school-aged children is asked, “Which of these three ice cream flavors do you like the most: vanilla, chocolate, or strawberry?” Describe a bar graph of their responses that would have the least amount of variability. Also describe a bar graph that would have the most variability.