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# 3.3 Mean, Median, Mode, Formulas

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Review of Mean, Median, and Mode, as well as the Rate Formula and Perimeter Formula.

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### 3.3 Mean, Median, Mode, Formulas

1. 1. Remember the 3 Ms? Mean, Median, and Mode ~Central Tendency~ Section 3.3 September 30, 2008 By Ms. D-H
2. 2. Mean? <ul><li>Mean: the sum of the data items divided by the number of data items. </li></ul><ul><li>These are data items: </li></ul><ul><li>2, 3, 4, 5, 8, 8, and 12 </li></ul><ul><li>2 + 3 + 4 + 5 + 8 + 8 + 12 </li></ul><ul><li>7 (total data items) </li></ul><ul><li>42 / 7 = the mean, which is 6 </li></ul>
3. 3. Median? <ul><li>Odd Number of Data Items : the middle number when the data items are put in numerical order. </li></ul><ul><li>Even Number of Data Items : the two middle numbers when data items are put in numerical order. </li></ul><ul><li>Median is the middle of the road </li></ul>
4. 4. Median? <ul><li>So find the median with these data items. </li></ul><ul><li>2, 3, 4, 5, 8, 8, and 12 </li></ul><ul><li>They’re in order </li></ul><ul><li>There are 7 numbers, meaning odd. </li></ul><ul><li>So which is the middle most number? </li></ul><ul><li>The median is 5. </li></ul>
5. 5. Mode? <ul><li>Mode: is the data item that occurs most often . </li></ul><ul><li>There can be one mode , multiple modes , or no mode . You can say how many modes there are too! </li></ul><ul><li>What about our previous data set? </li></ul><ul><li>2, 3, 4, 5, 8, 8, and 12 </li></ul><ul><li>8 is a mode for these data items. </li></ul>
6. 6. Find me the M, M & Ms <ul><li>12, 14, 26, 37, 8, and 14 </li></ul><ul><li>Re-order: 8, 12, 14, 14, 26, 37. </li></ul><ul><li>Mean: 18.5 </li></ul><ul><li>Median: 14 </li></ul><ul><li>How many Modes: 1 </li></ul><ul><li>Mode: 14 </li></ul>
7. 7. Find me the M, M & Ms <ul><li>2.3, 4.3, 3.2, 2.9, 2.7, and 2.3. </li></ul><ul><li>Re-order: 2.3, 2.3, 2.7, 2.9, 3.2, 4.3. </li></ul><ul><li>Mean: 2.95 </li></ul><ul><li>Median: 2.8 </li></ul><ul><li>How many Modes? 1 </li></ul><ul><li>Mode: 2.3 </li></ul>
8. 8. Find me ONLY Mode: <ul><li>Grape, grape, banana, nectarine, strawberry, strawberry, strawberry, orange, watermelon. </li></ul><ul><li>How many modes? </li></ul><ul><li>Just one: strawberry. </li></ul>
9. 9. How many modes? <ul><li>11, 9, 7, 7, 8, 8, 13, 11 </li></ul><ul><li>3 Modes </li></ul><ul><li>38.5, 55.4, 45.3, 38.5, 68.4 </li></ul><ul><li>1 Mode </li></ul>
10. 10. Outlier <ul><li>Outlier: is a data item (data value) that is much higher or lower than the other data values. </li></ul><ul><li>Outliers can affect the mean of a group of data. </li></ul><ul><li>Example: 2, 3.5, 1, 2.5, 5 billion. </li></ul><ul><li>Example: 35, 45, 40, 37, -6. </li></ul>
11. 11. Describing Data with M, M, & M. <ul><li>You can use what you know about Mean, Median, and Mode to describe data. </li></ul><ul><li>But figuring out which M describes it best is difficult. </li></ul>I think mode describes it best! Nah! Its got to be mean!
12. 12. Which M, M, & M is best? <ul><li>The favorite movie of students in the eighth grade class? </li></ul><ul><li>Mode: good for non-numerical data items and for frequent occurrences. </li></ul>
13. 13. Which M, M, & M is best? <ul><li>The distances students in your class travel to school. </li></ul><ul><li>Median: one student may live much further than everyone else. When an outlier may significantly influence the mean, we use median. </li></ul>
14. 14. Which M, M, & M is best? <ul><li>The daily high temperature during a week in July. </li></ul><ul><li>Mean: since daily temp. are not likely to have outlier, mean is best. When data have no outlier, use mean. </li></ul>
15. 15. Measures and Central Tendency <ul><li>Your text book is going to ask you determine which MEASURE of CENTRAL TENDENCY best describe the data. </li></ul><ul><li>Its just asking you to figure out which M works with the data best! </li></ul>
16. 16. Using Formulas Section 3.4 Just two formulas.
17. 17. Substituting into Formulas <ul><li>Formula is an equation that shows a relationship between quantities that are represented by variables. </li></ul><ul><li>Like: Susie has b books. b is the number of books Susie has. b stands for something. </li></ul>
18. 18. Rate <ul><li>Distance = rate • (time) </li></ul><ul><li>d = rt </li></ul><ul><li>Cause remember? r and t next to each other means you multiply them. </li></ul><ul><li>So…rate multiplied by time = distance. </li></ul>
19. 19. Obvious Example: d = r • t <ul><li>Suppose Ms. Dewey-Hoffman traveled 162 miles in 2 hours. Use the formula. </li></ul><ul><li>How fast was I going? What was my rate? </li></ul><ul><li>d = r • t </li></ul><ul><li>d = distance, or 162 miles. </li></ul><ul><li>t = time, or 2 hours. </li></ul><ul><li>162 miles = r • 2 hours. </li></ul>
20. 20. Obvious Example: d = r • t <ul><li>Suppose Ms. Dewey-Hoffman traveled 162 miles in 2 hours. Use the formula. </li></ul><ul><li>What was my rate? </li></ul><ul><li>162 miles = r • 2 hours . </li></ul><ul><li>2 hours 2 hours </li></ul><ul><li>162  2 = 82 miles/hour </li></ul><ul><li>So, Ms. Dewey-Hoffman was traveling at 82 miles/hour to go 162 miles in 2 hours. 82 mph is my r or rate. =] </li></ul>
21. 21. Try These: d = r • t <ul><li>d = 200 yards, t = 24 seconds </li></ul><ul><li>What don’t we know? Set up equation. Solve. </li></ul><ul><li>r = 30 feet/minute, t = 5 minutes </li></ul><ul><li>What don’t we know? Set up equation. Solve. </li></ul>
22. 22. Perimeter Formula: P = 2 l + 2 w . <ul><li>Perimeter = 2(length) + 2(width). </li></ul>W W L L <ul><li>The formula simplifies how the perimeter of a rectangle works. </li></ul><ul><li>Perimeter = l + l + w + w …so… </li></ul><ul><li>Perimeter = 2 l + 2 w </li></ul>
23. 23. Try These: Tell Me Perimeter <ul><li>Remember: P = 2l + 2w </li></ul><ul><li>Length = 16.8cm, Width = 27.3cm </li></ul><ul><li>Length = 8.6cm, Width = 17.4cm </li></ul>W L
24. 24. Assignment #16 <ul><li>Pages: 134-135: # 5-8 All, 15-18 All. </li></ul><ul><li>Pages: 139-140: # 5–21 Odd. </li></ul><ul><li>Make sure you answer ALL parts of each problem, the first set of problems ask for a lot. </li></ul>