1. Measures of Central Tendency Sixth Grade Mathematics 8-20-2009

2. Essential Questions What kinds of information do graphs provide? How can I use graphs to make comparisons? How can I use graphs to make predictions? How can graphs be misleading?

3. Measures of Central Tendency What are they? –Mean –Median –Mode Why are they important? –They can be used to analyze sets of data.

4. Mode Definition –The number that occurs most frequently in a set of data. Note: a number must occur at least twice to be considered a mode. If no number occurs more than once, then there is no mode. How is it found? –You create a frequency table.

5. Mode Example –Set: 4, 6, 6, 12 –Create a frequency table. –The mode for this set of data is 6.

6. Mode Now find the mode on your own for each of the previous sets of data. 2, 4, 5, 6, 8 11, 13, 13, 26 1, 1, 1, 1, 1, 2, 7, 7, 9, 13

7. Mode Answers –2, 4, 5, 6, 8 Mode = None No numbers occur more than once each. –11, 13, 13, 26 Mode = 13 13 occurs twice, the other numbers each occur once. –1, 1, 1, 1, 1, 2, 7, 7, 9, 13 Mode = 1 1 occurs 5 times, 7 occurs twice, the other numbers occur once.

8. Median Definition –The middle piece of data. How do you find it? –You must first place the numbers in numerical order. –Then you find the piece in the middle. –If there is an odd amount of numbers there will be a single number in the middle. That number is the median. –If there is an even amount of numbers the median will be the sum of the two numbers closest to the middle divided by 2.

9. Median Example –Set: 4, 6, 6, 12 –Place the set in numerical order It already is (but most times you will have to complete this step) –Find the middle: 4, 6, | 6, 12 –There is an even amount of numbers so the middle is between two numbers. –Find the sum of those two numbers and divide it by 2. 6 + 6 = 12 12 / 2 = 6 –The median for this set of data is 6.

10. Median Use the same sets of data from earlier to find the median of each. 2, 4, 5, 6, 8 10, 13, 13, 26 1, 1, 1, 1, 1, 2, 7, 7, 9, 13

11. Median Answers –2, 4, 5, 6, 8 Median = 5 –10, 13, 13, 26 Median = 13 13 + 13 = 26; 26 / 2 = 13 –1, 1, 1, 1, 1, 2, 7, 7, 9, 13 Median = 1.5 1 + 2 = 3; 3 / 2 = 1.5

12. Mean Definition –The mathematical average of a set of numbers. How is it found? –Find the sum of all the numbers in a set of data, then divide that sum by the amount of numbers in the set.

13. Mean Example –Set: 4, 6, 6, 12 –Find the sum: 4 + 6 + 6 + 12 = 28 –Divide the sum by the amount of numbers in the set: 28 / 4 = 7 –The mean for this set of data is 7.

14. Mean Now try some on your own. You may courteously discuss the process with your table. 2, 4, 5, 6, 8 11, 13, 13, 26 1, 1, 1, 1, 1, 2, 7, 7, 9, 13

15. Mean Answers –2, 4, 5, 6, 8 Mean = 25 / 5 = 5 –11, 13, 13, 26 Mean = 63 / 4 = 15.75 –1, 1, 1, 1, 1, 2, 7, 7, 9, 13 Mean = 43 / 10 = 4.3

16. Comparison 2, 4, 5, 6, 8 –Mean: 5; Median: 5; Mode: None 11, 13, 13, 26 –Mean: 15.75; Median: 13; Mode: 13 1, 1, 1, 1, 1, 2, 7, 7, 9, 13 –Mean: 4.3; Median: 1.5; Mode: 1