Practice

The height in feet of 25 trees is shown below (lowest to highest):
25, 27, 33, 34, 34, 34, 35, 37, 37, 38, 39, 39, 39, 40, 41, 45, 46, 47, 49, 50, 50, 53, 53, 54, 54.

The following data are daily high temperatures in a town for one month:
61, 61, 62, 64, 66, 67, 67, 67, 68, 69, 70, 70, 70, 71, 71, 72, 74, 74, 74, 75, 75, 75, 76, 76, 77, 78, 78, 79, 79, 95.

In a survey, several people were asked how many years it has been since they purchased a mattress. The results are shown in Table 2.41.

The students in Ms. Ramirez’s math class have birthdays in each of the four seasons. Table 2.43 shows the four seasons, the number of students who have birthdays in each season, and the percentage of students in each group. Construct a bar graph showing the number of students.

David County has six high schools. Each school sent students to participate in a county-wide science competition. Table 2.44 shows the percentage breakdown of competitors from each school and the percentage of the entire student population of the county that goes to each school. Construct a bar graph that shows the population percentage of competitors from each school.

65 randomly selected car salespersons were asked the number of cars they generally sell in one week. 14 people answered that they generally sell three cars, 19 generally sell four cars, 12 generally sell five cars, nine generally sell six cars, and 11 generally sell seven cars. Complete the table.

What does the relative frequency column in Table 2.45 sum to? Why?

What is the difference between cumulative relative frequency and relative frequency for each data value?

Construct a frequency polygon for the following.

1. Pulse Rates for Women	Frequency
   60–69	12
   70–79	14
   80–89	11
   90–99	1
   100–109	1
   110–119	0
   120–129	1

   Table 2.46

2. Actual Speed in a 30-MPH Zone	Frequency
   42–45	25
   46–49	14
   50–53	7
   54–57	3
   58–61	1

   Table 2.47

3. Tar (mg) in Nonfiltered Cigarettes	Frequency
   10–13	1
   14–17	0
   18–21	15
   22–25	7
   26–29	2

   Table 2.48

Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countries. Include an overlaid frequency polygon and discuss the shapes of the distributions, the center, the spread, and any outliers. What can we conclude about the life expectancy of women compared to men?

The following data sets list full-time police per 100,000 citizens along with incidents of a certain crime per 100,000 citizens for the city of Detroit, Michigan, during the period from 1961 to 1973.

1. Construct a double time series graph using a common x-axis for both sets of data.
2. Which variable increased the fastest? Explain.
3. Did Detroit’s increase in police officers have an impact on the incident rate? Explain.

Listed are 32 ages for Academy Award-winning best actors in order from smallest to largest:

18, 18, 21, 22, 25, 26, 27, 29, 30, 31, 31, 33, 36, 37, 37, 41, 42, 47, 52, 55, 57, 58, 62, 64, 67, 69, 71, 72, 73, 74, 76, 77

1. Find the percentile of 37.
2. Find the percentile of 72.

1. For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or a low percentile when running a race?
2. The 20^th percentile of run times in a particular race is 5.2 minutes. Write a sentence interpreting the 20^th percentile in the context of the situation.
3. A bicyclist in the 90^th percentile of a bicycle race completed the race in 1 hour and 12 minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the 90^th percentile in the context of the situation.

On an exam, would it be more desirable to earn a grade with a high or a low percentile? Explain.

In a survey collecting data about the salaries earned by recent college graduates, Li found that her salary was in the 78^th percentile. Should Li be pleased or upset by this result? Explain.

The University of California has two criteria used to set admission standards for freshman to be admitted to a college in the UC system:

1. Students' GPAs and scores on standardized tests (SATs and ACTs) are entered into a formula that calculates an admissions index score. The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12 percent of high school students in the state. In this context, what percentile does the top 12 percent represent?
2. Students whose GPAs are at or above the 96^th percentile of all students at their high school are eligible, called eligible in the local context, even if they are not in the top 12 percent of all students in the state. What percentage of students from each high school are eligible in the local context?

First quartile = ________

Third quartile = ________

10^th percentile = ________

Construct a box plot below. Use a ruler to measure and scale accurately.

Find the mean for the following frequency tables:

1. Grade	Frequency
   49.5–59.5	2
   59.5–69.5	3
   69.5–79.5	8
   79.5–89.5	12
   89.5–99.5	5

   Table 2.57

2. Daily Low Temperature	Frequency
   49.5–59.5	53
   59.5–69.5	32
   69.5–79.5	15
   79.5–89.5	1
   89.5–99.5	0

   Table 2.58

3. Points per Game	Frequency
   49.5–59.5	14
   59.5–69.5	32
   69.5–79.5	15
   79.5–89.5	23
   89.5–99.5	2

   Table 2.59

Identify the median.

sample mean = $\overline{x}$ = ________

mode = ________

16, 17, 19, 22, 22, 22, 22, 22, 23

When the data are skewed left, what is the typical relationship between the mean and median?

What word describes a distribution that has two modes?

Describe the relationship between the mode and the median of this distribution.

Figure 2.35

Describe the shape of this distribution.

Figure 2.37

Are the mean and the median the exact same in this distribution? Why or why not?

Figure 2.39

Describe the relationship between the mode and the median of this distribution.

Figure 2.41

The mean and median for the data are the same.

3, 4, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7

Is the data perfectly symmetrical? Why or why not?

Which is the least, the mean, the mode, and the median of the data set?

56, 56, 56, 58, 59, 60, 62, 64, 64, 65, 67

In a perfectly symmetrical distribution, when would the mode be different from the mean and median?

Find the value that is one standard deviation below the mean.

Use Table 2.60 to find the value that is three standard deviations

• above the mean, and
• below the mean