Transparency 2 Click the mouse button or press the Space Bar to display the answers.

Transparency 2a

8-4 Data Variability

Video Tutor Help Finding rangeFinding range (8-4) Box Plots (box and whiskers) Interquartile Range Khan Academy Box and whisker plot Finding mean

Video Tutor Help Identifying appropriate samples of a population Identifying bias in questions Estimating populations using capture/recapture

Worksheets Daily Notetaking Guide Worksheets Version A Practice, Guided Problem Solving Lesson 8-4 Practice 8-4 Guided Problem Solving 8-4

Vocabulary Practice Vocabulary 8A: Graphic Organizer Vocabulary 8B: Reading Comprehension Vocabulary 8C: Reading/Writing Math Symbols Vocabulary 8D: Visual Vocabulary Practice Vocabulary 8E: Vocabulary C Vocabulary 8F: Vocabulary Review Puzzle Vocabulary (Electronic) Flash Cards Measurement

Additional Lesson Examples Step-by-Step Examples Lesson 8-4

Lesson Readiness Lesson Quiz Problem of the Day Lesson 8-4

Measures of Variation Measures of variation are used to describe the distribution of the data.

Measures of Variation Range: the range of a set of data is the difference between the greatest and the least numbers in the set. Interquartile range: the range of the middle half of the data. It is the difference between the upper quartile and the lower quartile. (see next slide)

Interquartile Range Quartiles are the values that divide the data into four equal parts. The median separates the data in two equal parts Lower half Upper half median The median of the lower half of the set of data is the lower quartile (LQ) The median of the upper half of the set of data is the upper quartile (UQ) One half of the data lies between the lower quartile and the upper quartile

Interquartile Range 1, 2, 2, 3, 5, 6, 8, 9, 11 Median = = 8.5 LQ = UQ =

Outliers Data that are more than 1.5 times the value of the interquartile range beyond the quartiles are called outliers.

Interpreting Interquartile Range A small interquartile range means that the data in the middle of the set are close in value. A large interquartile range means that the data in the middle are spread out.

Example 3-1a Jobs The projected number of employees in 2008 in the fastest-growing occupations is shown. Display the data in a box-and-whisker plot. Fastest-Growing Jobs OccupationJobs (1000s) OccupationJobs (1000s) Computer Engineer 622Desktop Publishing 44 Computer Support 869Paralegal/Legal Assistant 220 Systems Analyst1194Home Health Aide1179 Database Administrator 155Medical Assistant 398 Source: U.S. Census Bureau Draw a Box-and-Whisker Plot

Example 3-1b Step 1Find the least and greatest number. Then draw a number line that covers the range of the data.

Example 3-1c Step 2Find the median, the extremes, and the upper and lower quartiles. Mark these points above the number line.

Example 3-1d Step 3Draw a box and the whiskers. Answer:

Example 3-1e Transportation The data listed below represents the time, in minutes, required for students to travel from home to school each day. Display the data in a box- and-whisker plot Answer:

Example 3-2a Weather The box-and-whisker plot below shows the average percent of sunny days per year for selected cities in each state. What is the smallest percent of sunny days in any state? Answer:The smallest percent of sunny days in any state is 23%. Interpret Data

Example 3-2b Weather The box-and-whisker plot below shows the average percent of sunny days per year for selected cities in each state. Half of the selected cities have an average percent of sunny days under what percent? Answer:Half of the selected cities have an average percent of sunny days under 56%. Interpret Data

Example 3-2c Weather The box-and-whisker plot below shows the average percent of sunny days per year for selected cities in each state. What does the length of the box in the box-and-whisker plot tell about the data? Answer:The length of the box is short. This tells us that the data values are clustered together. Interpret Data

Example 6-1a POPULATION Use the data in the table at the right to draw a box- and-whisker plot. 13.5Manila 14.4Cairo 16.2Los Angeles 17.9Osaka 17.9Bombay 17.9Sao Paulo 19.8Mexico City 19.9Seoul 20.2New York 34.8Tokyo Population (millions)City World’s Most Populous Cities Source: Time Almanac Draw a Box-and-Whisker Plot

Step 1Draw a number line that includes the least and greatest number in the data. Step 2Mark the extremes, the median, and the upper and lower quartile above the number line. Since the data have an outlier, mark the greatest value that is not an outlier. median Example 6-1a Step 3Draw the box and whiskers. Answer: Least valuelower quartile upper quartile Greatest value that is not an outlier outlier

Look over data – not sure if correct