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Warm-Up

Warm-Up. n = 6.125. Solve for x:. x = -11. Mean, Median, and Mode. By: Christina Carter . Math I. UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1-3 Today’s Question: How do we compare different sets of data? Standard: MM1D3.a. Mean

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Warm-Up

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  1. Warm-Up n = 6.125 Solve for x: x = -11

  2. Mean, Median, and Mode By: Christina Carter

  3. Math I UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1-3 Today’s Question: How do we compare different sets of data? Standard: MM1D3.a.

  4. Mean Also known as the average.  The mean is found by adding up all of the given data and dividing by the number of data entries. Example: the grade 10 math class recently had a mathematics test and the grades were as follows: 78, 66, 82, 89, 75, and 74 78 + 66 + 82 + 89 + 75 + 74 = 464 The mean average of the class is 464 / 6 = 77.3

  5. Mean Example: 1 Your parents want you to have at least an 80% test average in this class. So far, you have taken two tests, with scores of 78% and 75%. What must you earn on the third test to average 80%? x = 87

  6. Mean • Example: 2 • 12 of your friends eat a mean of 2.5 cookies. • Another group of 15 of your friends eat a mean of 3 cookies. • What is the mean number of cookies all your friends eat?

  7. Median The median is the middle number.  First you arrange the numbers in order from lowest to highest, then you find the middle number by crossing off the numbers until you reach the middle. Example: Find the median of 5, 9, 3, 7, 12 First, put them in order: 3, 5, 7, 9, 12 The median is the middle number: 3, 5, 7, 9, 12

  8. Median What if we have an even number of numbers? Find the median of : 66  74  75  78  82  89 There is no middle number.  What do we do? Take the two middle numbers and find the average, ( or mean ). 75 + 78 = 153 153 / 2 = 76.5                              The median is 76.5.

  9. Mode This is the number that occurs most often. Example: find the mode of the following data: 78  56  68  92  84  76  74  56  68  66  78  72  66 65  53  61  62  78  84  61  90  87  77  62  88  81                                                    The mode is  78.

  10. Range The range of a set of data is the largest number minus the smallest number. Example: Find the range of 5, 9, 3, 7, 12 First, put them in order: 3, 5, 7, 9, 12 The range is the largest minus the smallest: 12 – 3 = 9

  11. Best Measure of Central Tendency • Skew: Data that is not symmetrical when graphed in a bar chart. • Skew is caused by outliers, data that does not behave nicely. • Think of getting around 85% on three tests, and then getting a 20%. Calculated the mean and median of both data sets: Data Set A: 85, 85, 85 Data Set B: 85, 85, 85, 20 Which number would you want to tell you folks?

  12. Best Measure of Central Tendency • The outlier (20%) causes the data to be skewed left. • The outliers will pull the mean more than the median. • We really want to be able to use the mean of the data if possible. If the data is symmetrical (normal – a word we do not have yet), the best measure of central tendency is the mean. • If the data is skewed, the best measure of central tendency is the median. • Look at Problems 5 – 8 on page 365 asked “Which measure of spread is best to use?”

  13. pg 365 # 5 • Skewed to the right, so median would be the best choice for the measure of central tendency. • 86 86 87 89 96 100

  14. pg 365 # 6 • All the data points are pretty much in the same area, so the mean would be the best choice of measure of central tendency

  15. pg 365 # 7 • All the data points are pretty much evenly spread, so the mean would be the best choice measure of central tendency

  16. pg 365 # 8 • Skewed to the right, so median would be the best choice for the measure of central tendency.

  17. Got it? Cool! Do: “Mean Practice Problems” and pg 365, # 1 – 8 & 16

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