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Probability

Probability. January 07, 2013. Riddle Me This. What always runs but never walks, often murmurs, never talks, has a bed but never sleeps, has a mouth but never eats? A river. Kick Off. Order the numbers from least to greatest. 1. 7, 4, 15, 9, 5, 2 2. 70, 21, 36, 54, 22 Divide.

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Probability

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  1. Probability January 07, 2013

  2. Riddle Me This.. • What always runs but never walks, often murmurs, never talks, has a bed but never sleeps, has a mouth but never eats? • A river

  3. Kick Off Order the numbers from least to greatest. 1. 7, 4, 15, 9, 5, 2 2. 70, 21, 36, 54, 22 Divide. 2, 4, 5, 7, 9, 15 21, 22, 36, 54, 70 205 3. 820  4 65 4. 650  10 5. 1,125  25 45 6. 2,275 7 325

  4. Objective Learn to find the mean, median, mode, and range of a data set.

  5. Vocabulary mean median mode range outlier

  6. Helpful Hint The mean is sometimes called the average. Mean, Median, Mode, & Range The mean is the sum of the data values divided by the number of data items. The median is the middle value of anoddnumber of data items arranged inorder. For an even number of data items, the median is the average of the two middle values. The modeis the value or values that occur most often. When all the data values occur the same number of times, there is no mode. The range of a set of data is the difference between the greatest and least values. It is used to show the spread of the data in a data set.

  7. sum 8 items Mean, Median, Mode, & Range Additional Example 1: Finding the Mean, Median, Mode,and Range of Data Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 mean: Add the values. 4 + 7 + 8 + 2 + 1 + 2 + 4 + 2 = 30 Divide the sum by the number of items.  = 8 3.75 30 The mean is 3.75.

  8. Mean, Median, Mode, & Range Additional Example 1 Continued Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 median: Arrange the values in order. 1, 2, 2, 2, 4, 4, 7, 8 There are two middle values, so find the mean of these two values. 2 + 4 = 6 6  2 = 3 The median is 3.

  9. Mean, Median, Mode, & Range Additional Example 1 Continued Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 mode: The value 2 occurs three times. 1, 2, 2, 2, 4, 4, 7, 8 The mode is 2.

  10. Mean, Median, Mode, & Range Additional Example 1 Continued Find the mean, median, mode, and range of the data set. 4, 7, 8, 2, 1, 2, 4, 2 range: Subtract the least value 1, 2, 2, 2, 4, 4, 7, 8 from the greatest value. 8 – 1 = 7 The range is 7.

  11. sum 8 items Mean, Median, Mode, & Range Check It Out: Example 1 Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 mean: Add the values. 6 + 4 + 3 + 5 + 2 + 5 + 1 + 8 = 34 Divide the sum  = 34 8 4.25 by the number of items. The mean is 4.25.

  12. Mean, Median, Mode, & Range Check It Out: Example 1 Continued Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 median: Arrange the values in order. 1, 2, 3, 4, 5, 5, 6, 8 There are two middle values, so find the mean of these two values. 4 + 5 = 9 9  2 = 4.5 The median is 4.5.

  13. Mean, Median, Mode, & Range Check It Out: Example 1 Continued Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 mode: The value 5 occurs two times. 1, 2, 3, 4, 5, 5, 6, 8 The mode is 5.

  14. Mean, Median, Mode, & Range Check It Out: Example 1 Continued Find the mean, median, mode, and range of the data set. 6, 4, 3, 5, 2, 5, 1, 8 range: Subtract the least value 1, 2, 3, 4, 5, 5, 6, 8 from the greatest value. 8 – 1 = 7 The range is 7.

  15. Mean, Median, Mode, & Range

  16. 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 Mean, Median, Mode, & Range In the data set below, the value 12 is much less than the other values in the set. An extreme value such as this is called an outlier. 35, 38, 27, 12, 30, 41, 31, 35 x x x x x x x x

  17. Mean, Median, Mode, & Range Additional Example 3: Exploring the Effects of Outlierson Measures of Central Tendency The data shows Sara’s scores for the last 5 math tests: 88, 90, 55, 94, and 89. Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. Then tell which measure of central tendency best describes the data with the outlier. 55, 88, 89, 90, 94 outlier 55

  18. mean: median: mode: Mean, Median, Mode, & Range Additional Example 3 Continued With the Outlier 55, 88, 89, 90, 94 outlier 55 = 416 55+88+89+90+94 55, 88, 89, 90, 94 416  5 = 83.2 The median is 89. There is no mode. The mean is 83.2.

  19. mean: median: mode: Mean, Median, Mode, & Range Additional Example 3 Continued Without the Outlier 55, 88, 89, 90, 94 = 361 88+89+90+94 88, 89, 90, 94 + 2 361  4 = 90.25 = 89.5 The mean is 90.25. The median is 89.5. There is no mode.

  20. Caution! Since all the data values occur the same number of times, the set has no mode. Mean, Median, Mode, & Range

  21. Mean, Median, Mode, & Range Additional Example 3 Continued Adding the outlier decreased the mean by 7.05 and the median by 0.5. The mode did not change. The median best describes the data with the outlier.

  22. Mean, Median, Mode, & Range Check It Out: Example 3 Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. The tell which measure of central tendency best describes the data with the outlier. 63, 58, 57, 61, 42 42, 57, 58, 61, 63 outlier 42

  23. mean: median: mode: Mean, Median, Mode, & Range Check It Out: Example 3 Continued With the Outlier 42, 57, 58, 61, 63 outlier 42 = 281 42+57+58+61+63 42, 57, 58, 61, 63 281  5 = 56.2 The median is 58. There is no mode. The mean is 56.2.

  24. mean: median: mode: Mean, Median, Mode, & Range Check It Out: Example 3 Continued Without the Outlier 42, 57, 58, 61, 63 = 239 57+58+61+63 57, 58, 61, 63 + 2 239  4 = 59.75 = 59.5 The mean is 59.75. The median is 59.5. There is no mode.

  25. Mean, Median, Mode, & Range Check It Out: Example 3 Continued Adding the outlier decreased the mean by 3.55 and decreased the median by 1.5. The mode did not change. The median best describes the data with the outlier.

  26. Mean, Median, Mode, & Range • Choose a partner. One partner will get a SPS from the bin and a set of dice. Together you will complete the “Mean, Median, Mode Practice Activity” on the SPS. • When you are finished, raise your hand so that I can check your work. If you are correct, you may erase the SPS, return your materials to the bin, and begin your homework. If not, fix your mistakes and raise your hand to be checked again. • HW: WB 7-2, page 59

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