Chapter 1: Exploring Data
P2 #1 / Example #1 The table shows results of a poll asking adults whether they were looking forward to the Super Bowl game, the commercials, or didn’t plan to watch.Male / Female / Total
Game / 279 / 200 / 479
Commercials / 81 / 156 / 237
Won’t Watch / 132 / 160 / 292
Total / 492 / 516 / 1008
Construct a side-by-side bar chart for their preference based on gender. Note any trends that appear.
P2 #2 / Example #2 The data below give the number of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2008, as reported by NOAA.
3 / 2 / 1 / 2 / 4 / 3 / 7 / 2 / 3 / 3 / 2 / 5 / 2 / 2 / 4 / 2 / 2
6 / 0 / 2 / 5 / 1 / 3 / 1 / 0 / 3 / 2 / 1 / 0 / 1 / 2 / 3 / 2 / 1
2 / 2 / 2 / 3 / 1 / 1 / 1 / 3 / 0 / 1 / 3 / 2 / 1 / 2 / 1 / 1 / 0
5 / 6 / 1 / 3 / 5 / 3 / 3 / 2 / 3 / 6 / 7 / 2 / 6 / 8
a. Construct a dotplot.
b. Describe what you see in a few sentences.
1.1 #3 / Example #3 The data below give the amount of caffeine content (in milligrams) for an 8-ounce serving of popular soft drinks.
20 / 15 / 23 / 29 / 23 / 15 / 23 / 31 / 28 / 35 / 37 / 27 / 24 / 26 / 47 / 28 / 24 / 28 / 28
16 / 38 / 36 / 35 / 37 / 27 / 33 / 37 / 25 / 47 / 27 / 29 / 26 / 43 / 43 / 28 / 35 / 31 / 25
a. Construct stemplot.
b. Construct a split stemplot.
c. Describe what differences you notice from a and b.
Most people believe that you need to drink coffee or an energy drink to get good “buzz” off of the caffeine. Below is a table with common caffeine levels of tea, coffee, and energy drinks.
Coffee
133 / 160 / 150 / 103 / 150 / 93 / 150 / 115 / 75 / 75 / 40
Energy Drink
160 / 144 / 100 / 100 / 95 / 83 / 80 / 80 / 80 / 79
74 / 50 / 48
d. Make a back-to-back stemplot. Comment on the difference in caffeine levels between coffee and energy drinks.
1.1 #4 / Example #4:
Describe the distribution of the graph.
1.1 #5 / Example #5:
An executive finds the subscriptions (in millions of people) of the 20 leading American magazines is as follows:
Reader’s Digest / 17.9 / Ladies’ Home Journal / 5.3
TV Guide / 17.1 / National Enquirer / 4.7
National Geographic / 10.6 / Time / 4.6
Modern Maturity / 9.3 / Playboy / 4.2
AARP News Bulletin / 8.8 / Redbook / 4
Better Homes and Gardens / 8 / The Star / 3.7
Family Circle / 7.2 / Penthouse / 3.5
Woman’s Day / 7 / Newsweek / 3
McCall’s / 6.4 / Cosmopolitan / 3
Good Housekeeping / 5.4 / People Weekly / 2.8
Make a histogram for the number of subscriptions in intervals of 2 (million) compared to the frequency of that number. Then describe the graph.
1.1 & 1.2 #6 / Example #6:
The President of the United States has to be at least 35 years old and be born in America. Below is an ogive showing the relative cumulative frequency of the previous presidents that were inaugurated.
a. What percent of presidents were younger than 60?
b. What percent of presidents were between 50 and 55?
c. There is a horizontal line between 35 and 40 years of age. What does that mean?
d. What is the median age of the current presidents?
e. President Obama was 47 when he was inaugurated. What percent of presidents were older than him?
1.1 & 1.2 #7 / Example #7:
Identify any trends and describe the time plot.
1.1 & 1.2 #8 / Example #8:
Find the mean for the two sets of data.
Data set A: 1 1 2 2 3
Data set B: 1 1 2 2 500,000
1.1 & 1.2 #9 / Example #9
Calculate the Standard Deviation by Hand
Data Set: 6, 4, 4, 3, 2, 6, 101.1 & 1.2 #10 / Example #10
Using the numbers 1-10, choose 4 numbers so the standard deviation will be the smallest. Then choose 4 numbers so the standard deviation will be the largest. (Repeats are ok)
1.1 & 1.2 #11 / Example #11
Which graph will have the larger standard deviation? Why?
1.1 & 1.2 / Properties of the standard deviation and variance:
1. Sensitive to ______.
2. Some deviations are positive and some are negative (that’s why we square them!) Otherwise, they would add up to zero and tell us nothing about the deviance around the mean. Then, to get the original units, we take the square root.
3. Standard deviation is at least ZERO, or greater, but never ______.
4. Values that are very close together have a ______standard deviation and those far apart have a ______standard deviation.
1.2 # 12 / Example #12:
Find the median for the two sets of data.
Data set A: 1 1 2 2 3
Data set B: 1 1 2 2 500,000
Which one is a resistant measure? Mean or Median
1.2 # 13 / Example #13: The Fuel Economy of 2004 vehicles is given.
13 15 16 16 17 19 20 22 23 23 23 24 25
25 26 28 28 28 29 32 66
a. Determine the 5-number summary.
b. Calculate the range and IQR for each data set.
c. Make a box plot using the 5-number summary.
d. Describe the shape, center, and spread.
e. Are there any potential outliers using the criterion?
f. Construct a modified boxplot to account for the outlier.
Matching Histograms and Boxplots
Match each histogram with its boxplot, by writing the letter of the boxplot in the space provided.
1. ______/ A.
2. ______
/ B.
3. ______
/ C.
4. ______
/ D.
5. ______
/ E.
1.2 # 14 / Example #14:
Should you use the mean or median to discuss the center?
a. Average price of home
b. Average age
c. Average height
d. Average gas mileage for all cars
Matching Histograms and Summary Statistics
Match each histogram with a set of summary statistics, by writing the letter in the space provided.
1. ______/ A.
mean 10.5
standard deviation 1.4
median 10.7
IQR 2.0
2. ______
/ B.
mean 10.1
standard deviation 2.7
median 10.1
IQR 4.2
3. ______
/ C.
mean 10.2
standard deviation 2.1
median 10.5
IQR 2.5
4. ______
/ D.
mean 10.2
standard deviation 4.1
median 11.9
IQR 6.8
5. ______
/ E.
mean 8.8
standard deviation 2.8
median 8.0
IQR 1.9
1.2 # 15 / Example #15:
Consider the following data set: 1, 1, 1, 3, 4, 4, 5, 5
Transform the data.
Original Data / Multiply by 3 / Add 4
Mean
Median
S.D.
Q1
Q3
IQR
Range
Dotplot
Boxplot
1.2 # 16 / Example #16:
True or False.
a. If you add 7 to each entry on a list, that adds 7 to the mean.
b. If you add 7 to each entry on a list, that adds 7 to the standard deviation.
c. If you double each entry on a list, that doubles the mean.
d. If you double each entry on a list, that doubles the standard deviation.
e. Multiplying each entry on a list changes the mean.
f. Multiplying each entry on a list changes the standard deviation.
g. Adding to each entry on a list changes the mean.
h. Adding to each entry on a list changes the standard deviation.
1.2 # 17 / Example #17:
A college professor gave a test to his students. The test had five questions, each worth 20 points. The summary statistics for the students’ scores on the test are below. After grading the test, the professor realized that, because he had made a typographical error in question number 2, no student was able to answer the question. So he decided to adjust the students’ scores by adding 20 points to each one. What will be the summary statistics for the new, adjusted scores?
Summary Statistics for Scores / NEW
Mean / 62
Median / 60
Range / 45
Standard Deviation / 8
Q1 / 71
Q3 / 48
IQR / 23
1.2 # 18 / Example #18:
The summary statistics for the property tax per property collected by one county are below. This year, county residents voted to increase property taxes by 2 percent to support the local school system. What will be the summary statistics for the new, increased property taxes?
Summary Statistics for Property Tax / NEW
Mean / 12,000
Median / 8,000
Range / 30,000
Standard Deviation / 5,000
Q1 / 14,000
Q3 / 5,000
IQR / 9,000