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13.8 Interpret Box-and-Whisker Plots

13.8 Interpret Box-and-Whisker Plots. Essential Question: How do you make and interpret box-and-whisker plots?. 16, 16, no mode. ANSWER. 173.50, 173, 164. ANSWER. Lesson 13.8 , For use with pages 887-894. Warm-up Exercises. Find the mean, median, and mode(s) of the data.

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13.8 Interpret Box-and-Whisker Plots

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  1. 13.8 Interpret Box-and-Whisker Plots Essential Question: How do you make and interpret box-and-whisker plots?

  2. 16, 16, no mode ANSWER 173.50, 173, 164 ANSWER Lesson 13.8, For use with pages 887-894 Warm-up Exercises Find the mean, median, and mode(s) of the data. 1. 8, 12, 15, 17, 18, 26 2. 186, 144, 201, 164, 182, 164

  3. 3. The monthly charge for seven dial-up internet service providers are listed. What is the mean price? $10, $22, $17, $11, $16, $23, $25 about $17.71 ANSWER Lesson 13.8, For use with pages 887-894 Warm-up Exercises Find the mean, median, and mode(s) of the data.

  4. How would you cut an apple into fourths? • To find the Upper and Lower Quartiles: • Find the median (Middle Quartile) • Find the medians of the lower and upper halves • If two numbers are both in the middle remember to average them Upper and Lower Quartiles

  5. Draw a uniformly labeled number line • Place dots on: • Lower Extreme • Lower Quartile • Median • Upper Quartile • Upper Extreme • Draw a box enclosing the upper and lower quartile • Draw whiskers from the edge of each box to the extremes • Draw a line through the median Box-and-Whisker Plots

  6. A value widely separated from the rest of the data • Data must 1.5 times the Interquartile Range outside of the Interquartile Range • Interquartile Range = Upper Quartile – Lower Quartile Outliers

  7. Order: the data. Then find the median and the quartiles. EXAMPLE 1 Make a box-and-whisker plot Song Lengths The lengths of songs (in seconds) on a CD are listed below. Make a box-and-whisker plot of the song lengths. 173, 206, 179, 257, 198, 251, 239, 246, 295, 181, 261 SOLUTION STEP 1

  8. Plot: the median, the quartiles, the maximum value, and the minimum value below a number line. EXAMPLE 1 Make a box-and-whisker plot STEP 2 STEP 3 Draw: a box from the lower quartile to the upper quartile. Draw a vertical line through the median. Draw a line segment (a “whisker”) from the box to the maximum and another from the box to the minimum.

  9. Order: the data. Then find the median and the quartiles. 15, 20, 25, 30, 40, 55, 60, 70 for Example 1 GUIDED PRACTICE 1.Make a box-and-whisker plot of the ages of eight family members: 60, 15, 25, 20, 55, 70, 40, 30. SOLUTION STEP 1

  10. Plot: the median, the quartiles, the maximum value, and the minimum value below a number line. 10 20 30 40 50 60 70 80 90 100 . . . . 15 25 40 60 70 for Example 1 GUIDED PRACTICE STEP 2 STEP 3 Draw: a box from the lower quartile to the upper quartile. Draw a vertical line through the median. Draw a line segment (a “whisker”) from the box to the maximum and another from the box to the minimum.

  11. The box-and-whisker plots below show the normal precipitation (in inches) each month in Dallas and in Houston, Texas. EXAMPLE 2 Interpret a box-and-whisker plot Precipitation

  12. EXAMPLE 2 Interpret a box-and-whisker plot a.For how many months is Houston’s precipitation less than 3.5 inches? SOLUTION a. For Houston, the lower quartile is 3.5. A whisker represents 25% of the data, so for 25% of 12 months, or 3 months, Houston has less than 3.5 inches of precipitation.

  13. b. The median precipitation for a month in Dallas is 2.6 inches. The median for Houston is 3.8 inches. In general, Houston has more precipitation. For Dallas, the interquartile range is 3.2 – 2.3, or 0.9 inch. For Houston, the interquartile range is 4.4 – 3.= 5 0.9 inch. So, the cities have the same variation in the middle 50% of the data. The range for Dallas is greater than the range for Houston. When all the data are considered, Dallas has more variation in precipitation. EXAMPLE 2 Interpret a box-and-whisker plot b.Compare the precipitation in Dallas with the precipitation in Houston. SOLUTION

  14. 2. Precipitation for Example 2 GUIDED PRACTICE In Example 2, for how many months was the precipitation in Dallas more than 2.6 inches? SOLUTION For Dallas, the greater quartile is 2.6, A whisker represent 50% of the data, so for 50% of 12 months, or 6 months, Dallas has more than 2.6 inches of precipitation.

  15. EXAMPLE 3 Standardized Test Practice SOLUTION From Example 2, you know the interquartile range of the data is 0.9 inch Find 1.5 times the interquartile range: 1.5(0.9) = 1.35. From Example 2, you also know that the lower quartile is 2.3 and the upper quartile is 3.2. A value less than 2.3 – 1.35 = 0.95 is an outlier. A value greater than 3.2 + 1.35 = 4.55, is an outlier. Notice that 5.2 > 4.55.

  16. ANSWER The correct answer is B. EXAMPLE 3 Standardized Test Practice

  17. 3.0 5.4 3.0 and 5.4 No outlier for Example 3 GUIDED PRACTICE 3.Which value, if any, is an outlier in the data set ? 3.7, 3.0, 3.4, 3.6, 5.2, 5.4, 3.2, 3.8, 4.3, 4.5, 4.2, 3.7 SOLUTION The quartiles are 3.5, 3.75 and 4.4, The interquartile range is 4.4 – 3.5 = 1.9. An outlier must be 1.5(1.9) = 2.85 greater than the upper quartile (4.4 + 2.85 = 7.25) or less than the lower quartile (3.5 – 2.85 = 0.65). Since no number lies outside that range, the given data has no outlier and the correct answer is D.

  18. How do you make and interpret box-and-whisker plots? Essential Question:

  19. Benchmark Skills: • Finding Probabilities of Unordered Events Using Combinations • Finding Probabilities of Compound Events Quiz Retake – Lessons 13.3 to 13.4

  20. Textbook p. 896-900 Independent Practice

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