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Introductory Statistics Lesson 2.3 A

Introductory Statistics Lesson 2.3 A Objective: SSBAT find the mean, median, and mode of data. Standards: M11.E.2.1.1. Measure of Central Tendency A value (number) that represents a typical or central entry of a data set 3 commonly used measures are MEAN, MEDIAN, and MODE. Mean

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Introductory Statistics Lesson 2.3 A

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  1. Introductory Statistics Lesson 2.3 A Objective: SSBAT find the mean, median, and mode of data. Standards: M11.E.2.1.1

  2. Measure of Central Tendency • A value (number) that represents a typical or central entry of a data set • 3 commonly used measures are MEAN, MEDIAN, and MODE

  3. Mean • Add all of the numbers together and Divide by the number of values in the set Example: The ages of employees in a department are listed. What is the mean age? 34, 27, 50, 45, 41, 37, 24, 57, 40, 38, 62, 44, 39, 40 The mean age of the employees is 41.3 years.

  4. Population Mean  represents the population mean N  represents the number of entries in a Population

  5. Sample Mean  represents the sample mean n represents the number of entries in a Sample

  6. Example: The prices (in dollars) for a sample of roundtrip flights from Chicago, Illinois to Cancun, Mexico are listed. What is the mean price of the flights? 872, 432, 397, 427, 388, 782, 397  = 872 + 432 + 397 + 427 + 388 + 782 + 397 = 3695 = 527.90 The mean price of the flights is about $527.90.

  7. Median • The number that is in the middle of the data when it is ordered from least to greatest • Write the numbers in order from least to greatest • Find the middle number •  If there are 2 middle numbers, Add them and divide by 2

  8. Example: Find the Median of the flight prices from 1. 872, 432, 397, 427, 388, 782, 397  388, 397, 397, 427, 432, 782, 872  The Median flight price is $427.

  9. Example: The ages of a sample of fans at a rock concert are listed. Find the median age. 26, 27, 19, 21, 23, 30, 36, 21, 27, 19,

  10. Mode • The number that occurs the most in the data set • If no entry is repeated, there is No Mode • There may be more than 1 mode • Bimodal  A data set that has 2 modes

  11. Example: Find the mode of the flight prices from #1. 872, 432, 397, 427, 388, 782, 397  The mode price is $397. Example: Find the mode of the employee ages. 24, 27, 27, 34, 37, 38, 39, 40, 40, 44, 49, 57  The mode age is 27 and 40

  12. Example: A sample of people were asked which political party they belonged to. The results are in the table below. What is the Mode of their response?  The response with the greatest frequency is Republican therefore the MODE is Republican

  13. Example: Find the Mean, Median, and Mode Football Team Points Mean: 22.3 Median: 23.5 Mode: 13 and 24 Key: 1│2 = 12 points

  14. Example: Find the Mean, Median, and Mode • Entries: 1, 3, 3, 6, 6, 7, 8, 8, 8, 8, 10 • Mean: 6.2 • Median: 7 • Mode: 8

  15. Find the Mean, Median and Mode of the data set. 20, 20, 20, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 25, 25, 78 Mean, : 25.3 Median: 21.5 Mode: 20 Which measure of central tendency best describes this data set? Median

  16. Outlier • A data entry that is a lot bigger or smaller than the other entries in the set • Outliers cause Gaps in the data • Conclusions made from data with outliers can be flawed

  17. MEAN • There is only one mean for each data set • It is the most commonly • It takes into consideration all data entries • It is affected by Extreme Values – Outliers • MEDIAN • There is only one median for each data set • Extreme values (outliers) do NOT affect the median • MODE • Use when you are looking for the most popular item • Use when you have non-numerical data • When no value repeats there is no mode

  18. Homework Page 75 – 76 #18, 20, 22, 32, 34

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