Mean, Median, Mode, & Range Finding measures of central tendency 1 © 2013 Meredith S. Moody

Objective: You will be able to… Explain mean, median, mode, and range in your own words Find the mean, median, mode, and range of a set of data 2 © 2013 Meredith S. Moody

Vocabulary Measures of central tendency: Mathematical values that tell us where a data set is centered. The 3 measures are mean, median, and mode. 3 © 2013 Meredith S. Moody

Vocabulary : The average of the values in a set of data, found by adding all the values and dividing the sum by the total number of values Mean: The average of the values in a set of data, found by adding all the values and dividing the sum by the total number of values : The middle data value in a set of data, found by putting the data in numerical order and locating the middle value. For data that has no middle value, the median is the mean of the two middle numbers. Median: The middle data value in a set of data, found by putting the data in numerical order and locating the middle value. For data that has no middle value, the median is the mean of the two middle numbers. 4 © 2013 Meredith S. Moody

Vocabulary The most common data value, found by locating the value (or values) that occur(s) most often in a set of data. If no value occurs more than once, there is no mode. Mode: The most common data value, found by locating the value (or values) that occur(s) most often in a set of data. If no value occurs more than once, there is no mode. : The difference between the highest and lowest value in a set of data, found by subtracting the lowest data value from the highest data value Range: The difference between the highest and lowest value in a set of data, found by subtracting the lowest data value from the highest data value 5 © 2013 Meredith S. Moody

Vocabulary : A data value that is distinctly separate (much higher or much lower) than the rest of a set of data Outlier: A data value that is distinctly separate (much higher or much lower) than the rest of a set of data –For example, in the following set of data, 20 is an outlier 1, 3, 2, 5, 3, 20, 4, 2, 1, 6, 0 6 © 2013 Meredith S. Moody

Example: Mean A teacher gives a 20-point quiz and wants to find the measures of central tendency and the range of the scores. Here’s the score data: 18, 17, 19, 15, 10, 20, 18, 16, 14, 8 To find the mean, add all the data values, which equals 155 and divide by the total number of values (10), which equals 15.5; the average score on the quiz is © 2013 Meredith S. Moody

Example: Median Find the median by putting the data in numerical order 10, 14, 15, 16, 17, 18, 18, 19, 20 What if there were another data value, 13? Then the data has no middle number. Find the mean of the two middle numbers; that would be the median, = 33  33 ÷ 2 = © 2013 Meredith S. Moody

Examples: Mode & Range Find the mode of the data by looking at what number occurred most often –18 occurs twice; 18 is the mode Find the range by subtracting the lowest data value (10) from the highest data value (20) –The range is 20 – 10 = 10 9 © 2013 Meredith S. Moody

Making the mean, median, mode of it… Let’s gather the data of how many letters are in each student’s last name Let’s find the measures of central tendency of our data Mean = Median = Mode = Range = 10 © 2013 Meredith S. Moody

Guided practice 1 Find the mean, median, mode, and range of the following data set: 23, 47, 55, 62, 47, 57 –Mean: 48.5 –Median: 47 –Mode: 47 –Range: © 2013 Meredith S. Moody

Guided practice 2 Find the mean, median, mode, and range of the following data set: 17, 25, 27, 17, 32, 25, 83, 32, 102, 25 –Mean: 38.5 –Median: 26 –Mode: 25 –Range: © 2013 Meredith S. Moody

Choosing the right measure Why choose to find the mean? The mean offers a good summary of a data set when there are no outliers 13 © 2013 Meredith S. Moody

Choosing the right measure Why choose to find the median? The median gives a good summary of a data set if there are outliers 14 © 2013 Meredith S. Moody

Choosing the right measure Why choose to find the mode? The mode gives a good summary of the data when there are no outliers and most of the data points are the same 15 © 2013 Meredith S. Moody

Guided practice 1 Which measure of central tendency should we use for this set of data: 15, 13, 15, 15, 14, 15, 15 Mode … why? –There are no outliers and most of the data values are the same (only 2 values are not 15) 16 © 2013 Meredith S. Moody

Guided practice 2 Which should we use for this data: 30, 35, 31, 34, 37, 38, 34, 32, 33, 10? Median … why? –There is an outlier: © 2013 Meredith S. Moody

Guided practice 3 Which should we use for this data: 100, 98, 103, 97, 105, 99, 98, 103, 102, 101? Mean … why? –There are no outliers and the values are mostly different 18 © 2013 Meredith S. Moody

You try! Sam works for the US Census Bureau. He needs to find the measure of central tendency for the household income in the US. What measure should he use if there are no outliers? Why? –Mean: There are no outliers, and most of the values will be different 19 © 2013 Meredith S. Moody

You try! A 7 th grade teacher wants to find the measure of central tendency for the ages of her students. What measure should she use? Why? –Mode: It is unlikely there will be outliers, but most of the data values should be the same 20 © 2013 Meredith S. Moody

You try! Look at the data sets and decide which measure of central tendency to use – then use it to find the central tendency and explain why you used the measure you did 77, 75, 70, 75, 69 –Mean = 73.2: no outliers, different values 36, 2, 33, 38, 35, 31 –Median = 34: different values, outlier (2) 100, 102, 101, 100, 100, 103, 100 –Mode = 100: no outliers, mostly the same values 21 © 2013 Meredith S. Moody

Check In your own words, write an explanation of what mean, median, mode, and range are 22 © 2013 Meredith S. Moody