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11.5 Measures of Central Tendency

11.5 Measures of Central Tendency.

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11.5 Measures of Central Tendency

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  1. 11.5 Measures of Central Tendency 9.4.1.1 Describe a data set using data displays, such as box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics

  2. Guiding Question: How can I measure the variation and distribution of data? • Lesson Objective: I will find measures of central tendency, variation, and standard deviation for a set of data. • Key Words Mean Median Mode Expected Value Distribution Variance Standard Deviation Outlier

  3. Guiding Question: How can I measure the variation and distribution of data? • Define the following words • Mean • Median • Mode How do I find each one for a set of data? • How would you find the mean, median, and mode for this data set? {2, 3, 4, 2, 7, 5, 8, 6, 8, 3, 3, 5, 4, 5, 8, 3} Mean: Median: Mode:

  4. Guiding Question: How can I measure the variation and distribution of data? • An expected value is found by taking a weighted average of a set of data. • The probability distribution multiplies each outcome by its frequency. (Sum = 1) Example. 1. In baseball, slugging percentage is how many extra base hits you have per hit. (Single = 1, Homerun = 4). Joe Mauerhad 54 singles, 34 doubles, 5 triples, and 15 homeruns, what is his slugging percentage?

  5. Guiding Question: How can I measure the variation and distribution of data? • How do I make a box-and-whisker plot? • What are the 5 pieces I need to measure the spread of data? • What is the inter-quartile range (IQR)? • Make a box-and-whisker plot and find the IQR. {13, 14, 18, 13, 12, 17, 15, 12, 13, 19, 11, 14, 14, 18, 22, 23}

  6. Guiding Question: How can I measure the variation and distribution of data? • Standard Deviation and Variance – measure the spread of data • To find variance and standard deviation 1. Find the mean of the data 2. Subtract each value from the mean and square it 3. Add all the squares and divide it by # of values. (Variance) 4. Take the square root of the variance. (Standard Deviation) • Find the mean and standard deviation for the following {10, 12, 14, 15, 18, 20, 23}

  7. Guiding Question: How can I measure the variation and distribution of data? For the given set of data, lets find the mean, median, mode, make a box-and-whisker plot, and then find the variance and standard deviation. 35,33,31,34,29,30,29,26,24,25,23,23,20,17,17 Mean: Box and Whisker: Median: Mode: Variance: Std. Dev.:

  8. Guiding Question: How can I measure the variation and distribution of data? • Outlier – a value that does not belong, usually much larger or smaller than the rest of the data. • Usually the outlier is removed as it will skew the rest of the data. • In 2004, the New York Yankees scored this many runs in 6 games against the Red Sox. {3, 19, 4, 4, 2, 3} Which is the outlier? How does it affect the mean and standard deviation? (Calc)

  9. Find mean, median,mode, make a box-and-whisker plot, and find variance and standard deviation. 13, 17, 16, 17, 16, 20, 23, 21, 22, 22, 24, 26, 30, 30, 29 Mean: Box-and-Whisker Median: Mode: Variance: Std. Dev.:

  10. Assignments Pg. 833 13-19 Pg. 833 20, 22-23, 25, 26 Pg. 833 29-37, 39, 41-43, 49-51

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