.Grade 6
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Introducing the Concept

Data

Subtopic 1: Measures of Central Tendency: Mean, Median, and Mode Introducing the Concept Your students may have encountered the mean, median and mode before, but it's a good idea to review how to find them again. Mean, median or mode is used by statisticians to find one number which is representative of all the numbers in the data set. Discuss with your students the difficulty in finding one number which would be representative of all the numbers. Prerequisite Skills and Concepts: Students should be able to put a set of numbers in ascending and descending order and perform simple calculations using the four basic operations. Write the following numbers on the board: 6, 3, 2, 5, 8, 15, 1, 2, 4, 5, 16, 2 Say: These numbers are the number of runs scored in 12 games played by a middle-school baseball team. I'd like us to analyze them for more information. What might I do with the data to help analyze the information? Students might suggest a number of things, such as making a graph, putting them in order, finding the mean, median, or mode for the number of runs per game, etc. If they don't, suggest some of those ideas to them. Say: Someone suggested putting the numbers in order. Let's do that. Have a volunteer come to the board and put the data in order from least to greatest. 1, 2, 2, 2, 3, 4, 5, 5, 6, 6, 14, 16 Ask: Now that we have the data in order, which one of the measures of central tendency would be easy to find from this list? (the median) How would I go about finding the median? Students should say that since there are 12 numbers, the median is the average of the sixth and seventh number, which is 4.5. Ask: Great. What else is easy to find from the data on the board? (the mode) What is the mode for a set of data? (It is the number most frequently repeated.) So what is the mode in this set of data? (2) Ask: How would I find the mean for this data? (Add all the numbers and divide by 12.) At your desks, find the mean for the data. Indicate that the sum of the numbers is 66 and the mean is 5.5. Ask: Are there any numbers which are either much less or greater than most of the other numbers? (Yes, 14 and 16) Numbers like this are called outliers, because they are distant from most of the other numbers. What might have caused this to happen? Students may say the team didn't have a good pitcher for those games or their defense was weak or something similar. Say: Let's disregard the games with 14 and 16 runs and investigate the mean, median, and mode again. Would the mode change? (No, it still would be 2.) Ask: What would the median be? (3.5) Find the mean for the new data. Give the students time to compute the mean. The sum of the 10 numbers is 36 and the mean is 3.6. Be sure the students divide by 10 and not 12, since there are only 10 numbers in the new set of data. Ask: So what happened when we got rid of some outliers which were greater than most of the other data? (The median and mean got smaller and the mode didn't change.) Say: Depending on the specific data, we can't always be sure the mode will stay the same or that the median will become less, but we can be sure that the mean will get smaller if we eliminate outliers which are greater than most of the data. What do you think would happen to the mean of a set of data if we eliminated data which were much less than the mean? Students should say that the mean will increase.

      Measures of Central Tendency:
      Mean, Median, and Mode

      Sampling Techniques

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