8.3.0: Exercises

Use the steam-and-leaf plot below to answer the questions. Round all answers to three decimal places.

0	1 1 1 2 6 6 7
1	0 0 0 0 2 5 5 9
2	0 0 5 9
3	0 5
4	0

Exercise \(\PageIndex{1}\)

Find the mode.

Exercise \(\PageIndex{2}\)

Find the median.

Exercise \(\PageIndex{3}\)

Find the mean.

Use the stem-and-leaf plot below to answer the following questions. Round all answers to three decimal places.

7	8
8	0 6
9	1 1 4 8
10	0 0 3 5 9
11	0 0 1 1 1 2 6 8
12	0 1 5

Exercise \(\PageIndex{4}\)

Find the mode.

Exercise \(\PageIndex{5}\)

Find the median.

Exercise \(\PageIndex{6}\)

Find the mean.

The following table shows the frequency distribution for a number of countries visited by students. Use this table to answer the questions, rounding all answers to three decimal places.

Number of Countries	Frequency
0	13
1	11
2	5
3	1

Exercise \(\PageIndex{7}\)

Find the mode of the number of countries visited.

Exercise \(\PageIndex{8}\)

Find the median of the number of countries visited.

Exercise \(\PageIndex{9}\)

Find the mean of the number of countries visited.

The following table shows the frequency distribution for the number of fumbles by a selection of football players. Use this table to answer the questions, rounding all answers to three decimal places.

Number of Fumbles	Frequency
0	5
1	13
2	3
3	4

Exercise \(\PageIndex{10}\)

Find the mode of the number of fumbles.

Exercise \(\PageIndex{11}\)

Find the median of the number of fumbles.

Exercise \(\PageIndex{12}\)

Find the mean of the number of fumbles.

A public opinion poll about an upcoming election asked respondents, “How many political advertisements do you recall seeing on television in the last 24 hours?” Use this data to answer the questions, rounding all answers to three decimal places.

6	2	5	5	2	2	4	1	3	0	1	2	1	6	2
5	2	4	8	6	3	3	4	2	5	3	4	2	2	3

Exercise \(\PageIndex{13}\)

Compute the mode.

Exercise \(\PageIndex{14}\)

Compute the median.

Exercise \(\PageIndex{15}\)

Compute the mean.

For the following exercises, use the data found in “TNSchools”, which has data on many institutions of higher education in the state of Tennessee. Here are what the columns represent:

Column Name	Description
AdmRate	Proportion of applicants that are admitted
UGEnr	Number of undergraduate students
PTUG	Proportion of undergraduates who attend part-time
InState	Tuition and fees for in-state students
OutState	Tuition and fees for out-of-state students
FacSal	Mean monthly faculty salary
Pell	Proportion of students receiving Pell Grants
MedDebt	Median student loan debt at degree completion
StartAge	Mean age at the time of entry
Female	Proportion of students who identify as female

(source: https://data.ed.gov)

Exercise \(\PageIndex{16}\)

What is the mean undergraduate enrollment at these schools?

Exercise \(\PageIndex{17}\)

What is the median undergraduate enrollment at these schools?

Exercise \(\PageIndex{18}\)

Generate a histogram for undergraduate enrollment, and use it to describe the effect of the distribution on the mean and the median as measures of centrality.

Exercise \(\PageIndex{19}\)

What is the mean proportion of part-time undergraduates at these schools?

Exercise \(\PageIndex{20}\)

What is the median proportion of part-time undergraduates at these schools?

Exercise \(\PageIndex{21}\)

Generate a histogram for proportion of part-time undergraduates, and use it to describe the effect of the distribution on the mean and the median as measures of centrality.

Exercise \(\PageIndex{22}\)

What is the mean of the monthly faculty salaries at these schools?

Exercise \(\PageIndex{23}\)

What is the median of the monthly faculty salaries at these schools?

Exercise \(\PageIndex{24}\)

Generate a histogram for the monthly faculty salaries, and use it to describe the effect of the distribution on the mean and the median as measures of centrality.

The dataset “AvgSAT” gives the average SAT score for incoming students (the use of “average” here stands in for “mean” to avoid confusion in the following problems) for every institution in the United States that reported the data (from data.ed.gov). Use that dataset to answer the following questions.

Exercise \(\PageIndex{25}\)

What is the mean of the average SAT scores?

Exercise \(\PageIndex{26}\)

What is the median of the average SAT scores?

Exercise \(\PageIndex{27}\)

Construct a histogram of average SAT scores, and describe how the distribution affects the mean and the median.

For the following exercises, use the table, which gives the final results for the 2021 National Women’s Soccer League season. The columns are standings points (PTS; teams earn three points for a win and one point for a tie), wins (W), losses (L), ties (T), goals scored by that team (GF), and goals scored against that team (GA).

Team	Points	W	L	T	GF	GA
Portland Thorns FC	44	13	6	5	33	17
OL Reign	42	13	8	3	37	24
Washington Spirit	39	11	7	6	29	26
Chicago Red Stars	38	11	8	5	28	28
NJ/NY Gotham FC	35	8	5	11	29	21
North Carolina Courage	33	9	9	6	28	23
Houston Dash	32	9	10	5	31	31
Orlando Pride	28	7	10	7	27	32
Racing Louisville FC	22	5	12	7	21	40
Kansas City Current	16	3	14	7	15	36

(source: http://www.nwslsoccer.com)

Exercise \(\PageIndex{28}\)

Compute the mode(s), median, and mean of points.

Exercise \(\PageIndex{29}\)

Compute the mode(s), median, and mean of wins.

Exercise \(\PageIndex{30}\)

Compute the mode(s), median, and mean of losses.

Exercise \(\PageIndex{31}\)

Compute the mode(s), median, and mean of ties.

Exercise \(\PageIndex{32}\)

Compute the mode(s), median, and mean of goals scored (GF).

Exercise \(\PageIndex{33}\)

Compute the mode(s), median, and mean of goals against (GA).

For the following exercises, use the data in “CUNY” (taken from data.ed.gov, which gives proportions of degrees awarded in various disciplines) to answer the given questions:

Exercise \(\PageIndex{34}\)

Compute the median and mean proportions of degrees awarded in Information Science.

Exercise \(\PageIndex{35}\)

Compute the median and mean proportions of degrees awarded in Education.

Exercise \(\PageIndex{36}\)

Compute the median and mean proportions of degrees awarded in Humanities.

Exercise \(\PageIndex{37}\)

Compute the median and mean proportions of degrees awarded in Biology.

Exercise \(\PageIndex{38}\)

Compute the median and mean proportions of degrees awarded in Physical Science.

Exercise \(\PageIndex{39}\)

Compute the median and mean proportions of degrees awarded in Social Science.

---