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Analyzing Data: Mean, Median, Mode, IQR, and Standard Deviation

Calculate statistical values for a room's age data with 5 people twice. Explore impact of a 99-year-old entering the room on the values. Learn about resistant and nonresistant statistics, outliers, and Box Plots. Understand the relationship between Mean and Median.

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Analyzing Data: Mean, Median, Mode, IQR, and Standard Deviation

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  1. Warm – Up Find the Mean, Median, Mode, IQR and Standard Deviation of the age of a room containing 5 people. Ages: 16, 18, 17, 16, 19. Calculate all values a second time. Describe what happens to these values if someone’s 99 year old Grandma walks into the room. Mean = Mode = Median = Standard Dev. = IQR = 17.2 16 17 1.304 2.5 Mean = Mode = Median = Standard Dev. = IQR = 30.833 16 17.5 33.415 3

  2. CHAPTER 5 (continued) The Mean and the Std. Dev. are considered NONRESISTANT because they’re very sensitive and influenced by extreme outliers. The Median, IQR, and Mode are considered RESISTANT or ROBUST, since outliers do not ‘greatly’ (if at all) affect their value.

  3. CHAPTER 5 (continued) The Mean in relation to the Median • If the Mean is (roughly) equal to the Median then the distribution is approximatelysymmetric. • If the Mean is greater than the Median then the distribution is skewed right. • If the Mean is less than the Median then the distribution is skewed left. A = Mode B = Median C = Mean A = Mode A = Median A = Mean C = Mode B = Median A = Mean

  4. Unbiased – Statistics are unbiased when the center of the distribution is approximately equal to the true population average. Biased - True population mean. Unbiased and small spread are the best. You can generalized only if the data was RANDOMLY collected from entire population.

  5. Min. Q1 Med. Q3 Max. The Five Number Summary: Minimum, Q1, Median, Q3, Maximum The Five Number Summary can be displayed in a BOX PLOT (A Box and Whisker Plot)

  6. Calculate the Mean, Standard Deviation, and 5-Number summary. Then constructing a Box Plotwith the following data: Babe Ruth’s # of Home Runs with the New York Yankees 1920-1934 54 59 35 41 46 25 47 60 54 46 49 46 41 34 22 Mean = 43.933 Standard Dev. = 11.247 Min = 22, Q1 = 35 Median = 46 Q3 = 54, Max = 60 35 Q1 46 Med. 54 Q3 60 Max. 22 Min. # of Ruth’s Home Runs

  7. What is an OUTLIER ?

  8. Formula to Determine Outliers: An Observation, xi, is an Outlier if: xi> Q3 + 1.5(IQR) or xi< Q1 – 1.5(IQR) Determine if any Outliers exist for #H.Runs: 54 59 35 41 46 25 47 60 54 46 49 46 41 34 22 Xi > Q3 + 1.5∙(IQR) = Xi > 54 + 1.5(54 – 35) = 82.5 Xi < Q1 - 1.5∙(IQR) = Xi < 35 - 1.5(54 – 35) = 6.5 Q1 = 35 Q3 = 54 IQR = 19

  9. HW: #4, 15, 17 on REVIEW sheet.

  10. HW: Page 92:14, 16, 22 22.

  11. HW: Page 92:14, 16, 22

  12. HW: Page 92:14-24 even March/April February July The Med. for June is higher and more consistent than Jan. Summer months have more consistent temp.

  13. The Modified Box Plot represents Outliers outside of the Box Plot.

  14. Example of Box Plot for Multiple data Sets Heights of Plant (mm)

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