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3.1 Measures of Center

3.1 Measures of Center. Objectives: By the end of this section, I will be able to… Calculate the mean for a given data set. Find the median, and describe why the median is sometimes preferable to the mean. Find the mode of a data set. Describe how skewness affects these measures of center.

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3.1 Measures of Center

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  1. 3.1 Measures of Center Objectives: By the end of this section, I will be able to… • Calculate the mean for a given data set. • Find the median, and describe why the median is sometimes preferable to the mean. • Find the mode of a data set. • Describe how skewness affects these measures of center.

  2. St. Andrews St. Elizabeth’s St. Joseph's Prep, Philly St. Marks St. Thomas More Tatnall Tower Hill Ursuline Wilmington Christian Aquinas Archmere Cardinal O'Hara, Phillly Father Judge, Philly Malvern Prep, Philly Monsignor Bonner, Philly Padua Red Lion Salesianum Sanford Wilmington Friends Caravel Tuitions of Area High Schools GROUP 2 GROUP 1

  3. Tuition Activity • Estimate the tuition of your school. Hint: All tuitions fall between $4,000 and $50,000. 2) Write your estimate on your slip of paper. 3) Get into the two groups and get in order from the lowest tuition to the highest tuition.

  4. Find the Median • Each student on the end says “One” • The next two students say “Two” • The next two students say “Three” • Keep going until you find the middle person, or the median tuition. • Report your median tuition to the class. • Find the mean of your tuitions.

  5. Three Measures of Central Tendency • Mean (sample mean): average of a data set • Median: middle number of a data set • Mode (modal): most frequent data point

  6. Mean (or sample mean) • Symbol is • Formula to find the mean • n = total number of items • Σ= Greek letter SIGMA and means SUM

  7. Mean (or sample mean) • The mean is SENSITIVE to Extreme Values, called OUTLIERS. • Why? 90, 92, 91, 87, 90, 95, 96, 93, 88, 87, 46

  8. Median • Always put data items in ORDER FIRST! • Then find the middle term of the data set • If there is no exact middle, find the average of the TWO MIDDLE TERMS.

  9. Median • The median is NOT sensitive to OUTLIERS. • Why? 90, 92, 91, 87, 90, 95, 96, 93, 88, 87, 46 46, 87, 87, 88, 90, 90, 91, 92, 93, 95, 96

  10. Mode • Order data first • Find the data point that occurs the most • You do not have to have a mode • You can have more than one mode

  11. Write down what you think the average tuition is for area private high schools. • Find the mean, median, and mode of the tuitions of area high schools.

  12. Skewness and Measures of Center • For RIGHT-skewed distributions, the mean > median. • For LEFT-skewed distributions, the mean < median. • For SYMMETRIC distributions, the mean = median (roughly)

  13. Finding values on Calculator • Input data into STAT → EDIT → LIST • Then Quit (2nd MODE) and go to HOME SCREEN Find the MEAN • 2nd STAT → MATH → 3.MEAN • 2nd 1 to get L1. Hit ENTER. Find the MEDIAN • 2nd STAT → MATH → 4.MEDIAN • 2nd 1 to get L1. Hit ENTER

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