1. CALCULATING Mean, Median, Mode, and Range The Practical Application and Purpose for Value Comparison Kristina Hereford, IISME 2012 SRI International Center for Technology in Learning Math Research Associate

2. THE PRACTICAL APPLICATION OF DATA - Collecting Raw Data is the first step of performing analysis. - Once you have the data, there are four common ways of comparing the set of information: Mean, Median, Mode, and Range. - Calculating these four values provides a common base of comparison so that multiple people can compare and contrast the information. - Trends and Patterns can also be easily discovered when these values are compared.

3. THE PURPOSE OF VALUE COMPARISON - Businesses pay organizations like SRI and the CTL to make sense of the information for them. - Mathematicians, Social Scientists, Computer Engineers, Economists, and Teachers work together to provide their respective insights on how to find meaningful patterns and trends. - Organizing responses by kind and depth of detail and calculating how many of each response were two ways to make sense of the raw data. - With the data analyzed (Mean, Median, Mode, Range, and other interesting patterns observed), the companies that come to SRI International or the CTL can then return to their customers and share how and why this information is important to them.

4. SSOOO… Let’s Get Calculating

5. MEAN DEFINITION: The average value for a set of data points. TO CALCULATE: Take the SUM of all the numbers in the set and DIVIDE by the number of data point there are in the set. WHY IMPORTANT?: The Mean is the most common value of comparison. Having an average of a set of numbers is the most common way to compare various sets of data with one another.

6. 13, 15, 11, 11, 5, 12, 3 13 + 15 +11 + 11 + 5 + 12 + 3 = 70 70 / 7 = 10 First, find the sum of the data. Then divide by the number of data points. The mean is 10 EXAMPLE#1

7. One way you can remember that “MEAN” means to AVERAGE because the “mean teacher averages your grade.” Mean

8. An electronics store sells MP3 players at the following prices: $350, $275, $500, $325, $100, $375, and $300. EXAMPLE#2 What is the MEAN price for a MP3 Player?

9. $2225 / 7 = $317.86 First, find the sum of the data. Then divide by the number of data points. The MEAN price for a MP3 Player is $317.86 EXAMPLE#2 $350 + $275 + $500 + $325 + $100 +$375 + $300 = $2225

10. MEDIAN DEFINITION: The MIDDLE number in an ordered set of data. TO CALCULATE: First ORGANIZE all the numbers in numerical sequence, and then LOCATE the number in the middle of the data set. NOTE: If there is an even # of items, ADD the two middle numbers and DIVIDE by two, and that answer is the Median. WHY IMPORTANT?: The Median is similar to the Mean in that it is a value that can provide more general information about a data set.

11. First, ORGANIZE the numbers in numerical order. Then LOCATE the number in the middle. The MEAN in this set is 11 EXAMPLE#3A (ODD # of data items) 13, 15, 11, 11, 5, 12, 3 3, 5, 11, 11, 12, 13, 15

12. First, ORGANIZE the numbers in numerical order. Then LOCATE the number in the middle. Since there are TWO, you must ADD and then DIVIDE. The MEAN in this set is 11.5 EXAMPLE#3B (EVEN # of data items) 13, 15, 11, 5, 12, 3 3, 5, 11, 12, 13, 15 11 + 12 = 23 23 / 2 = 11.5

13. An electronics store sells MP3 players at the following prices: $350, $275, $500, $325, $100, $375, and $300. EXAMPLE#4 What is the MEDIAN price for a MP3 Player?

14. First, ORGANIZE the numbers in numerical order. Then LOCATE the number in the middle. The MEDIAN price for the MP3 Player is $325 EXAMPLE#4 $100, $275, $300, $325, $350, $375, $500

15. One way you can remember that “MEDIAN” means the MIDDLE is because “the median is the name of the central divider on the freeway, that is in the middle of the road”

16. MODE DEFINITION: The data item that appears MOST often than any other data item. TO CALCULATE: COUNT and IDENTIFY which kind of data point has the most items. The highest number that appears in the set is the Mode. WHY IMPORTANT?: The Mode is useful when determining probability or analyzing the data set for what occurs most frequently.

17. Which number in the data set appears the most? 13, 15, 11, 11, 5, 12, 3 The MODE in this set is 11 EXAMPLE#5A

18. Sometimes there are multiple numbers that appear the same amount of times. 13, 5, 15, 11, 11, 5, 12, 3, 13 The MODES in this set are 5, 11, 13 EXAMPLE#5B NOTE: if you see that there are multiple modes, putting the numbers in numerical order first is very helpful. 3, 5, 5, 11, 11, 12, 13, 13

19. Sometimes there is NO MODE when each data item is listed the same number of times (usually once). 13, 15, 11, 5, 12, 3 There is NO MODE in this set. EXAMPLE#5C

20. An electronics store sells MP3 players at the following prices: $350, $275, $500, $325, $100, $375, and $300. EXAMPLE#6 What is the MODE price for a MP3 Player?

21. $100, $275, $300, $325, $350, $375, $500 In this data set, each MP3 Player has a different cost. There is NO MODE in this set. Putting the data set in numerical order…

22. One way you can remember that “MODE” means MOST is because “MODE sounds like MOST” OR BEACUSE they’re both shorter words

23. RANGE DEFINITION: The DIFFERENCE between the GREATEST and LEAST numbers in a data set. TO CALCULATE: Organize the data set in numerical order. IDENTIFY the Highest and Lowest values, and SUBTRACT them. The answer is the Range, or the difference/distance between the two end points in the data set. WHY IMPORTANT?: The Range is useful when determining the end points or the amount of information that is included in a data set. Depending on the purpose of the data set Ranges can be large or small, providing broad or more detailed information.

24. 13, 15, 11, 11, 5, 12, 3 3, 5, 11, 11, 12, 13, 15 15 – 3 = 12 Then SUBTRACT the High from the Low The RANGE in this data set is 12 EXAMPLE#7 Putting the data set in numerical order…

25. An electronics store sells MP3 players at the following prices: $350, $275, $500, $325, $100, $375, and $300. EXAMPLE#8 What is the RANGE of prices for a MP3 Player?

26. High = $500, Low = $100 $500-$100 = $400 Then SUBTRACT the High from the Low The RANGE in this data set is $400 EXAMPLE#8 Putting the data set in numerical order… $100, $275, $300, $325, $350, $375, $500

27. One way you can remember that “RANGE” means DISTANCE between the end points is because “ a field (AKA range) is far and wide (AKA distance)” LOW (bottom, far) HIGH (top, wide)

28. MEDIAN In the Middle MEANAverage MODEMost RANGE High – Low (Boundaries of the Set)