mean, median and mode - math geek mama...to explain/define/discuss mean, median and mode or outlier...

Mean, Median

And Mode

A Math Investigation by:

Bethany @ MathGeekMama.com

Teaching Tips:

• If you don’t have enough pennies, use the attached sets of data. Try not to give everyone the same set though, as there will be better discussion if students have different outcomes and dot plots.

• This is meant to be an introduction to measures of center, so there is no need to explain/define/discuss mean, median and mode or outlier before the investigation. Let students work and discuss these on their own first.

• You will want to make sure to discuss the procedure for finding the median when

the data set is even, however, so that everyone uses the same method: Find the two middle numbers, add them together and divide by two.

• Make sure students don’t get hung up on numbering their dot plot. Encourage

them to just use just the last two digits rather than the full date, or to just label every 5 or 10 years rather than labeling every single year.

• As soon as students begin to notice outliers, encourage them to think about

and discuss the effects rather than giving them a definition.

• After students are finished and are discussing the “best” measure, encourage them to think about different situations. For example, when measuring distance or miles per gallon, etc. mean is the most useful, but when discussing family income, median is a better tool, and when ordering class t-shirts, mode would be the most helpful.

• For further discussion you may want to ask students what other measures might

be helpful when analyzing their data set and making conclusions. For example, the minimum or maximum or the range.

I hope you find this resource useful! J

© www.MathGeekMama.com

Penny Mint Years Data Set:

1987, 1972, 1990, 2001, 2012, 1986, 2004, 1997, 1994, 2002, 2010, 1986, 2003, 1997, 2012, 1964, 1983, 1975, 2014, 1983, 2008, 2012, 2001, 1988


1985, 1973, 1990, 2001, 2011, 1985, 2004, 1994, 1994, 2003, 2010, 1986, 2003, 1995, 2012, 1962, 1983, 1977, 2011, 1983, 2008, 2012, 2001


1987, 1974, 1994, 2000, 2012, 1986, 2002, 1997, 1994, 1962, 2000, 1983, 2000, 1997, 2011, 1964, 1983, 1972, 2014, 1983, 2001, 1966, 1988


1987, 1972, 1990, 1988, 1982, 1986, 1999, 1997, 1994, 1975, 1972, 1986, 1965, 1997, 1971, 1964, 1983, 1975, 1966, 1983, 1998, 1976, 1982


1985, 1982, 1990, 2001, 2012, 1984, 2004, 1997, 1994, 2002, 2010, 1986, 2003, 1997, 2012, 1961, 1983, 1985, 2014, 1983, 2008, 2012, 2001, 1998


1989, 1972, 1990, 2001, 1998, 1986, 2000, 1997, 1994, 2002, 2001, 1987, 2000, 1997, 2015, 1963, 1988, 1995, 2001, 1987, 1986, 1994, 2001


1986, 1972, 1990, 2008, 2012, 1985, 2006, 1997, 1994, 2002, 2012, 1983, 2013, 1996, 2012, 1966, 1952, 1975, 2014, 1968, 2007, 2010, 2001, 1984


Name: ______________________________


Summarizing Data: An Investigation

Before you Begin: To summarize a large amount of data with one number is to use the measure of center. For example, “Americans watch an average of 4 hours of t.v. a day,” or “Half the participants polled have 4 or more people in their household,” or “When asked how many extracurricular activities students participated in, the most frequent answer was 2.” These are examples of using the mean, or average, median, or middle, and the mode, or most frequent value, to describe findings in a set of data. For this Invest igation You wi l l Need: 20-30 pennies

Step 1: Sort your pennies by year. Make a dot plot of the years on a number line. Be sure to label the number line, t it le the plot and show units used.

Step 2: Now arrange your pennies in a line from oldest to newest. Find the median, or middle value. 1. Does your median have to be a whole-number year (no decimals)? Why or why not? 2. Would you get the same median if you arranged your pennies from newest to oldest? Why?

Step 3: On your dot plot, c irc le the value that represents the median.

Step 4: Now stack all the pennies from the same year. The stack that is the tallest is called the mode. If there are 2 tall stacks, your data set is bimodal. However, if all your stacks are the same (1 of each or 2 of each) you would say there is no mode because 1 is not more than all the others. 1. Does your set of pennies have a mode (or more than 1?)? What is the mode (or modes) of your set? 2. Does the mode have to be a whole-number year (no decimals)? Why or why not?

Step 5: Draw a square around the mode (or modes) on your dot plot.

Step 6: Find the sum of all the years of your pennies, and then divide by the total number of pennies. This number is called the mean. 1. What is the mean of your data set? 2. Are there any values that seem to make a significant impact on your mean? What happens to your mean if you remove that number(s)? 3. Based on this set of data, what measure of center seems to be the best and most helpful in describing the data set?

Step 7: Draw an arrow to the mean value on your dot plot and label it mean.


Think About It…

1. When are the mean, median and mode close to being the same? 2. What measure of center do you feel is the best or most accurate description of a data set? What factors might affect your answer? 3. When a single data point is far removed from the rest of the set it is known as an out l ier . Did you have any outliers? Is there ever a case when an outlier does not affect the mean? 4. If you purchase 15 items at the grocery store and the average price per item is $1.37, what was your total bi l l? Explain how you found your answer.

Now Practice… Find the median, mode and mean for each of the following data sets.

1. {1, 5, 7, 3, 5, 9, 6, 8, 10} 2. {12, 6, 11, 7, 18, 5, 2, 21} 3. {6, 1, 3, 9, 2, 7, 3, 4, 8, 8, 4} 4. {10, 10, 20, 20, 20, 25, 40, 35, 20}


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mean, median and mode - math geek mama...to explain/define/discuss mean, median and mode or outlier...

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