Chapter 3 Data Description Section 3-3 Measures of Variation

Range

Variance

Sample Variance

Sample Standard Deviation

Shortcut

Find the range. Section 3-3 Exercise #7

Is the data consistent or does it vary? Explain.

Finding the Sample Variance and Standard Deviation for Grouped Data

f Number Section 3-3 Exercise #21

Class f

Section 3-3 Exercise #33

Chebyshev’s theorem

The Empirical (Normal) Rule Chebyshev’s theorem applies to any distribution regardless of its shape. However, when a distribution is bell-shaped (or what is called normal), the following statements, which make up the empirical rule, are true. Approximately 68% of the data values will fall within 1 standard deviation of the mean. Approximately 95% of the data values will fall within 2 standard deviations of the mean. Approximately 99.7% of the data values will fall within 3 standard deviations of the mean.

Section 3-3 Exercise #41

Chapter 3 Data Description Section 3-4 Measures of Position

A z score or standard score for a value is obtained by subtracting the mean from the value and dividing the result by the standard deviation. The symbol for a standard score is z. The formula is

Section 3-4 Exercise #13

Percentile Formula

Section 3-4 Exercise #22

Section 3-4 Exercise #23

Chapter 3 Data Description Section 3-5 Exploratory Data Analysis

The Five-Number Summary and Boxplots

A boxplot is a graph of a data set obtained by drawing a horizontal line from the minimum data value to Q1, drawing a horizontal line from Q3 to the maximum data value, and drawing a box whose vertical sides pass through Q1 and Q3 with a vertical line inside the box passing through the median or Q2.

Minimum: Q1:Q1: Median: Q3:Q3: Maximum: Interquartile Range: Data arranged in order: Identify the five number summary and find the interquartile range. 8, 12, 32, 6, 27, 19, 54 Section 3-5 Exercise #1

Section 3-5 Exercise #9

1. a. If the median is near the center of the box, the distribution is approximately symmetric. b. If the median falls to the left of the center of the box, the distribution is positively skewed. c. If the median falls to the right of the center, the distribution is negatively skewed. 2. a. If the lines are about the same length, the distribution is approximately symmetric. b. If the right line is larger than the left line, the distribution is positively skewed. c. If the left line is larger than the right line, the distribution is negatively skewed. Information Obtained from a Boxplot

Section 3-5 Exercise #15

Data arranged in order :

50,000 52,435 62,850 66,500 77,700 78,008 92, ,628 United States 46,563 56, , , , ,539 South America Section 3-5 Exercise #16