MTH 243 Introduction to Probability and Statistics
Summer 2012
Measures of Center (Section 2.1)
1. The following list gives the high temperatures in 36 US cities on July 20, 2012 (source:
http://www.nws.noaa.gov/xml/tpex/scs.php).
CITY
HI
ABILENE TX
AKRON CANTON
ALBANY NY
ALBUQUERQUE
ALLENTOWN
AMARILLO
ANCHORAGE
ASHEVILLE
ATLANTA
ATLANTIC CITY
AUSTIN
BALTIMORE
BATON ROUGE
BILLINGS
BIRMINGHAM
BISMARCK
BOISE
BOSTON
BRIDGEPORT
BROWNSVILLE
BUFFALO
BURLINGTON VT
CARIBOU
CASPER
CHARLESTON SC
CHARLESTON WV
CHARLOTTE
CHATTANOOGA
CHEYENNE
CHICAGO
CINCINNATI
CLEVELAND
COLORADO SPGS
COLUMBIA SC
COLUMBUS GA
COLUMBUS OH
a.
b.
c.
d.
93
92
94
100
95
92
60
86
88
95
90
98
89
73
87
72
82
97
92
87
85
95
85
72
86
94
93
91
68
95
90
91
77
91
89
93
Find the mean of the data:
Find the median of the data:
Find the mode of the data:
Throw out the lowest value and recalculate the mean, median and mode using only the
remaining 35 values.
i. New mean:
ii. New median:
iii. New mode:
MTH 243 Introduction to Probability and Statistics
Summer 2012
e. Discuss how the mean, median, and mode are affected by extreme values (high or low).
Construct another (small – about 5 data points) set of data to illustrate your ideas.
2. Construct a data set where the mean = median = mode.
3. Construct a data set where the mean > median.
4. Make a general statement about a characteristic of the data you might if the mean > median.
5. Most parents brag that their child is “above average”. Is it possible for say, 80% of a data set to be
above the average (mean)? Construct a data set where this is so.
MTH 243 Introduction to Probability and Statistics
Summer 2012
6. Do problem 7 on page 16 of your book.
7. Which measure of center (mean, median, or mode) would best describe the following sets of data?
Give justifications for your answers.
a. The typical size of shoe sold in a store. ____________________________
b. The typical weights of football players on a team. _____________________
c. The typical cost of homes in a community. ______________________
d. The typical age of 7 people in a family if six of them are under 40 and one is 96 years
old.___________________
e. The typical price of a textbook in a bookstore.__________________
8. Recall that µ is the symbol representing the population mean (parameter) and 𝑥̅ (xbar) is the sample
mean (statistic). For each of the following write µ or 𝑥̅ next to it to indicate if it most likely represents
a population or sample mean, respectively.
a. The average number of letters per word in the Gettysburg Address by Abraham Lincoln is
4.29. _____
b. The average number of red skittles in a pack of Skittles is 4.56. _____
c. The average number of 8-oz cups of coffee Americans drink per day is 3.1. _____
d. The average number of red skittles in my 4 packages of Skittles is 3.5. _____
9. Find the mean, median and mode of the following data set: