## Descriptive Statistics Homework

Attempt these practice problems and then check your answers. Note that not every part of these problems has an included solution.

### Exercises

1. Forty randomly selected students were asked the number of pairs of sneakers they owned. Let $X$= the number of pairs of sneakers owned. The results are as follows:

X Frequency Relative Frequency Cumulative Relative Frequency
1 2
2 5
3 8
4 12
5 12
7 1

Table 2

1. Find the sample mean $\overline x$
2. Find the sample standard deviation, $s$
3. Construct a histogram of the data.
4. Complete the columns of the chart.
5. Find the first quartile.
6. Find the median.
7. Find the third quartile.
8. Construct a box plot of the data.
9. What percent of the students owned at least five pairs?
10. Find the 40th percentile.
11. Find the 90th percentile.
12. Construct a line graph of the data
13. Construct a stem plot of the data

2. Following are the published weights (in pounds) of all of the team members of the San Francisco 49ers from a previous year

177; 205; 210; 210; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174; 185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270; 280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215;185; 230; 250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265

1. Organize the data from smallest to largest value.
2. Find the median.
3. Find the first quartile.
4. Find the third quartile.
5. Construct a box plot of the data.
6. The middle 50% of the weights are from _______ to _______.
7. If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?
8. If our population were the San Francisco 49ers, would the above data be a sample of weights or the population of weights? Why?
9. Assume the population was the San Francisco 49ers. Find:
i. the population mean, $μ$.
ii. the population standard deviation, $σ$.
iii. the weight that is 2 standard deviations below the mean.
iv. When Steve Young, quarterback, played football, he weighed 205 pounds. How many standard deviations above or below the mean was he?
10. That same year, the average weight for the Dallas Cowboys was 240.08 pounds with a standard deviation of 44.38 pounds. Emmit Smith weighed in at 209 pounds. With respect to his team, who was lighter, Smith or Young? How did you determine your answer?
3. In a recent issue of the IEEE Spectrum, 84 engineering conferences were announced. Four conferences lasted two days. Thirty-six lasted three days. Eighteen lasted four days. Nineteen lasted five days. Four lasted six days. One lasted seven days. One lasted eight days. One lasted nine days.
Let X = the length (in days) of an engineering conference.

1. Organize the data in a chart.
2. Find the median, the first quartile, and the third quartile.
3. Find the 65th percentile.
4. Find the 10th percentile.
5. Construct a box plot of the data.
6. The middle 50% of the conferences last from _______ days to _______ days.
7. Calculate the sample mean of days of engineering conferences.
8. Calculate the sample standard deviation of days of engineering conferences.
9. Find the mode.
10. If you were planning an engineering conference, which would you choose as the length of the conference: mean; median; or mode? Explain why you made that choice.
11. Give two reasons why you think that 3 - 5 days seem to be popular lengths of engineering conferences.

##### Try these multiple choice questions. Exercises (4 - 10)
The next three questions refer to the following information. We are interested in the number of years students in a particular elementary statistics class have lived in California. The information in the following table is from the entire section.

Number of years
Frequency
7 1
14 3
15 1
18 1
19 4
20 3
22 1
23 1
26 1
40 2
42 2
Total = 20

4. What is the IQR?
A. 8
B. 11
C. 15
D. 35

5. What is the mode?
A. 19
B. 19.5
C. 14 and 20
D. 22.65

6. Is this a sample or the entire population?
A. sample
B. entire population
C. neither

The next two questions refer to the following table. $X$ = the number of days per week that 100 clients use a particular exercise facility.

X Frequency
0 3
1 12
2 33
3 28
4 11
5 9
6
4

Table 13

7. The 80th percentile is:
A. 5
B. 80
C. 3
D. 4

8. The number that is 1.5 standard deviations BELOW the mean is approximately:
A. 0.7
B. 4.8
C. -2.8
D. Cannot be determined

The next two questions refer to the following histogram. Suppose one hundred eleven people who shopped in a special T-shirt store were asked the number of T-shirts they own costing more than $19 each. **** 9. The percent of people that own at most three (3) T-shirts costing more than$19 each is approx-
imately:
A. 21
B. 59
C. 41
D. Cannot be determined

10. If the data were collected by asking the first 111 people who entered the store, then the type of sampling is:
A. cluster
B. simple random
C. stratied
D. convenience

Source: Barbara Illowsky and Susan Dean, https://resources.saylor.org/wwwresources/archived/site/wp-content/uploads/2011/06/MA121-1.3.4-hw.pdf