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Contemporary Mathematics

# Chapter Review

## Gathering and Organizing Data

Decide whether randomization is being used in the selection of these samples. If it is, identify the type of random sample (simple, systematic, cluster, or stratified).

1 .
College students want to gauge interest in a new club they're thinking about starting. They choose three residence halls at random and slide a survey form under the door to every room.
2 .
The managers of a campus dining hall want feedback on a new dish that is being served, so they ask the first 10 people who choose that dish what they think of it.
3 .
The administration of a large university system with five campuses wants to administer a survey to students in the system. The administration chooses 50 students at random from each campus; the 250 students selected form thesample.

4 .
A sample of college students were asked how many of their meals were provided by a campus dining hall on the previous day. Here are the results:
 0 1 0 3 2 3 3 2 2 0 2 1 1 0 0 1 2 0 3 0 1 3 2 3 0 1 3 0

Create a frequency distribution for these data.

## Visualizing Data

5 .
Create a bar chart to visualize the data in question 4.
6 .
Use the data in “MBB2019” on every school that fielded an NCAA Division I men’s basketball team in the 2018–2019 season, to create a histogram of the number of free throws made by each team (FT).

## Mean, Median and Mode

7 .
The data below show the top ten scorers (by points per game) in the National Basketball Association for the 2018–2019 season. Find the mode, median, and mean age of these players without technology.
Rank Player Age
1 James Harden 29
2 Paul George 28
3 Giannis Antetokounmpo 24
4 Joel Embiid 24
5 Stephen Curry 30
6 Devin Booker 22
7 Kawhi Leonard 27
8 Kevin Durant 30
9 Damian Lillard 28
10 Bradley Beal 25
Table 8.13 (source: https://www.basketball-reference.com/leagues/NBA_2019_leaders.html)
8 .
Using the data in “MBB2019”, find the mean, median, and mode of the number of free throws made by each team (FT).

## Range and Standard Deviation

9 .
Using the data in “MBB2019”, find the range and standard deviation of the number of free throws made by each team (FT).

## Percentiles

Use the data in “MBB2019”, to answer the following:

10 .
What number of free throws (FT) is at the 40th percentile?
11 .
At what percentile is Syracuse University, which made 480 free throws?

## The Normal Distribution

12 .
Identify the means and standard deviations of these normal distributions:

Answer the following about data that are distributed normally with mean 200 and standard deviation 20:

13 .
What proportion of the data are between 160 and 240?
14 .
What’s the standardized score of the data value 235?
15 .
At what percentile would the data value 187 fall?
16 .
What data value would be at the 90th percentile?

## Applications of the Normal Distribution

Use the data in “MBB2019” to answer the following:

17 .
What is the standardized score for Purdue Universitiy’s number of free throws (FT = 461)?
18 .
At what percentile would we estimate Purdue’s value of FT to fall, using the normal distribution?
19 .
At what percentile does Purdue’s value of FT actually fall?

## Scatter Plots, Correlation, and Regression Lines

For each of the following scatter plots, decide whether linear regression would be appropriate. If it is, classify the strength and direction of the relationship.

20 .
21 .
22 .
Use the data in “NBA2019” to answer the following:
23 .
What is the correlation coefficient between the number of field goals attempted per game (FGA) and number of points scored per game (PTS)?
24 .
What is the equation of the regression line we would use to predict PTS from FGA?
25 .
Write a sentence to interpret the slope of the regression line.
26 .
Predict the number of points per game for a player who attempts 16 field goals per game.
27 .
Danilo Gallinari attempted 13 field goals per game, and averaged 19.8 points per game. Did he score more or fewer points per game than expected? By how much?
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