## 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

- How to calculate

- 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

- Density Curves

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:

- Textbook
- Ch. 1, p. 40-44

- Preview
- Normal Calculations: AgainstAllOdds_StudentGuide_Unit08
- Checking Assumptions of Normality: AgainstAllOdds_StudentGuide_Unit09