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**