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Worksheet on Averages - Solutions

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The average of a data set is a measure of its center. Despite the common use of the word average, this descriptive statistic can be found in one of four different ways: the mean, median, mode or midrange. The following problems can be used to practice calculating these statistics for sets of data taken from the real world.

Worksheet on Averages

1. The ages of the presidents when they were first inaugurated President of the United States are given in the list below:


Washington - 57, J. Adams - 61, Jefferson - 57, Madison - 57, Monroe - 58, J. Q. Adams - 57, Jackson - 61, Van Buren - 54, W. H. Harrison - 68, Tyler - 51, Polk - 49, Taylor - 64, Fillmore - 50, Pierce - 48, Buchanan - 65, Lincoln - 52, A. Johnson - 56, Grant - 46, Hayes - 54, Garfield - 49, Arthur - 50, Cleveland - 47, B. Harrison - 55, McKinley - 54, T. Roosevelt - 42, Taft - 51, Wilson - 56, Harding - 55, Coolidge - 51, Hoover - 54, F. D. Roosevelt - 51, Truman - 60, Eisenhower - 62, Kennedy - 43, L. B. Johnson - 55, Nixon - 56, Ford - 61, Carter - 52, Reagan - 69, G.H.W. Bush - 64, Clinton - 46, G. W. Bush - 54, Obama - 47

A. What is the mean age? 54.6 years

B. What is the median age? 54 years

C. What is the mode of the ages? 54 years

D. What is the midrange? 56 years

2. The time in days of the orbits of the planets is given by: Mercury - 88,Venus - 225, Earth - 365, Mars - 687, Jupiter - 4337, Saturn - 10760, Uranus - 30700, Neptune - 60200, Pluto - 90780.

A. What is the mean orbit? 20016 days

B. What is the median orbit? 4337 days

C. What is the mode of the orbits? None

D. What is the midrange? 45434 days

3. The monthly precipitation in inches at Waco, Texas in 2010 is given by the following: January - 5.29, February - 3.47, March - 4.63, April - 4.03, May - 0.89, June - 5.72, July - 3.35, August - 0.42, September - 9.49, October - 0.99, November - 1.05, December - 0.77.

A. What is the mean precipitation? 3.34 inches

B. What is the median precipitation? 3.41 inches

C. What is the mode of the precipitation data? None

D. What is the midrange? 4.96 inches

4. The populations in millions of the states of the U.S. are given by:


California - 36.4, Texas - 23.5, New York - 19.3, Florida - 18.1, Illinois - 12.8, Pennsylvania - 12.4, Ohio - 11.5, Michigan - 10.1, Georgia - 9.4, North Carolina - 8.9, New Jersey - 8.7, Virginia - 7.6, Massachusetts - 6.4, Washington - 6.4, Indiana - 6.3, Arizona - 6.2, Tennessee - 6.0, Missouri - 5.8, Maryland - 5.6, Wisconsin - 5.6, Minnesota - 5.2, Colorado - 4.8, Alabama - 4.6, South Carolina - 4.3, Louisiana - 4.3, Kentucky - 4.2, Oregon - 3.7, Oklahoma - 3.6, Connecticut - 3.5, Iowa - 3.0, Mississippi - 2.9, Arkansas - 2.8, Kansas - 2.8, Utah - 2.6, Nevada - 2.5, New Mexico - 2.0, West Virginia - 1.8, Nebraska - 1.8, Idaho - 1.5, Maine - 1.3, New Hampshire - 1.3, Hawaii - 1.3, Rhode Island - 1.1, Montana - .9, Delaware - .9, South Dakota - .8, Alaska - .7, North Dakota - .6, Vermont - .6, Wyoming - .5

A. What is the mean of the of all of the state populations? 6.0 million

B. What is the median population? 4.25 million

C. What is the mode of the population data? 1.3 million

D. What is the midrange? 18.45 million

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