Lesson 3: Standard Deviation and Normal Curves

August 30, 2017

Review:

  • Measures of Center
  • Boxplots
  • Slack
  • Attendance

Presentation:

  • Standard Deviation
    • How to calculate
      • See formulas on pp. 40-41
      • Example 1.19 on p. 41
      • Video
      • Demonstrate with student height data
  • Normal Curves
    • Density Curves
      • Height of curve indicates proportion of values
      • Area under the curve = 1.0
        • Any sub-area under the curve is then a proportion (% of values)
    • Normal Curves
      • A special case of density curves
      • Bell shaped and symmetrical
      • Mean and Standard deviation
      • 68 – 95 – 99.7 Rule
      • Video
      • Demonstrate with student height data

Assignment:

Problem 1. Below are the number of home runs that Babe Ruth hit in each of his 15 years with the New York Yankees, 1920 – 1934.
54 59 35 41 46 25 47 60 54 46 49 46 41 34 22 

Calculate the mean and standard deviation

Problem 2. Six ninth-grade students and six 12th-grade students were asked: How many movies have you seen this month? Here are their responses.
Ninth-grade students: 5, 1, 2, 5, 3, 8
12th-grade students: 4, 2, 0, 2, 3, 1

Calculate the mean and standard deviation for each of these data sets. Which is more spread out, the ninth-grade or 12th-grade data set?

Problem 3. Height of 4-year-old boys is approximately normally distributed with mean μ = 40 inches and standard deviation σ = 1.5 inches. Sketch a copy of this curve. On the horizontal axis, mark the location of the mean. Then mark points on the horizontal axis that are one standard deviation on either side of the mean.

Problem 4. IQ scores are normally distributed with mean 100 and standard deviation 15.

Sketch a copy of this curve. Then on the horizontal axis mark the mean, 100, and one standard deviation on either side of the mean. Label the horizontal axis as IQ Test Scores. Scores above 120 represent superior intelligence. Shade the area under your normal curve that represents the proportion of people with superior intelligence.

Study:

Justin

Justin Holman is CEO of Aftermarket Analytics, where he leads efforts to develop cutting edge sales forecasting and inventory optimization technology for the Automotive Aftermarket. Prior to joining Aftermarket Analytics, Justin managed corporate consulting for the Strategy & Analytics division at MapInfo Corporation, leading major projects for retail clients including The Home Depot, Darden Restaurants, Bridgestone-Firestone, Sainsbury’s and New York & Company. Before that, Justin served as Vice President of Software Development at LogicTools, now part of IBM's supply chain application software group. Justin holds a B.A. from Claremont McKenna College, a Ph.D. from the University of Oregon and an Executive Management certificate from Northwestern University's Kellogg School of Management.

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