2. Why use boxplots? ease of construction convenient handling of outliers construction is not subjective (like histograms) Used with medium or large size data sets (n > 10) useful for comparative displays

3. Disadvantage of boxplots does not retain the individual observations should not be used with small data sets (n < 10)

4. How to construct find five-number summary Min Q1 Med Q3 Max draw box from Q1 to Q3 draw median as center line in the box extend whiskers to min & max

5. Modified boxplots display outliers fences mark off mild & extreme outliers whiskers extend to largest (smallest) data value inside the fence ALWAYS use modified boxplots in this class!!!

6. Inner fence Q1 – 1.5IQRQ3 + 1.5IQR Any observation outside this fence is an outlier! Put a dot for the outliers. Interquartile Range (IQR) – is the range (length) of the box Q3 - Q1

7. Modified Boxplot... Draw the “whisker” from the quartiles to the observation that is within the fence!

8. Outer fence Q1 – 3IQRQ3 + 3IQR Any observation outside this fence is an extreme outlier! Any observation between the fences is considered a mild outlier.

9. For the AP Exam...... you just need to find outliers, you DO NOT need to identify them as mild or extreme. Therefore, you just need to use the 1.5IQRs

10. A report from the U.S. Department of Justice gave the following percent increase in federal prison populations in 20 northeastern & mid-western states in 1999. 5.91.35.05.94.55.64.16.34.86.9 4.53.57.26.45.55.38.04.47.23.2 Create a modified boxplot. Describe the distribution. Use the calculator to create a modified boxplot.

11. Symmetrical boxplots Approximately symmetrical boxplot Skewed boxplot

12. Evidence suggests that a high indoor radon concentration might be linked to the development of childhood cancers. The data that follows is the radon concentration in two different samples of houses. The first sample consisted of houses in which a child was diagnosed with cancer. Houses in the second sample had no recorded cases of childhood cancer.

13. Cancer 10 21 5 23 15 11 9 13 27 13 39 22 7 20 45 12 15 3 8 11 18 16 23 16 9 57 16 21 18 38 37 10 15 11 18 210 22 11 16 17 33 10 No Cancer 9 38 11 12 29 5 7 6 8 29 24 12 17 11 11 3 9 33 17 55 11 29 13 24 7 11 21 6 39 29 7 8 55 9 21 9 3 85 11 14 Create parallel boxplots. Compare the distributions.

14. Cancer’s 5 # Summary: No Cancer’s 5 # Summary: MinQ1MedQ3Max 3111622210 IQR = 11 MinQ1MedQ3Max 38.511.526.585 IQR = 18

15. Calculating the fence (Cancer): Q1 – 1.5 IQR 11 – 1.5*11 = - 5.5 Q3 + 1.5 IQR 22 + 1.5*11 = 38.5 Calculating the fence (No Cancer): Q1 – 1.5 IQR 8.5 – 1.5*18 = -18.5 Q3 + 1.5 IQR 26.5 + 1.5*18 = 53.5

16. Creating a Box Plot 050100150200 Radon Cancer No Cancer

17. Cancer No Cancer 100 200 Radon The median radon concentration for the no cancer group is lower than the median for the cancer group. The range of the cancer group is larger than the range for the no cancer group. Both distributions are skewed right. The cancer group has outliers at 39, 45, 57, and 210. The no cancer group has outliers at 55 and 85.

18. Creating a Box Plot on your Calculator

19. Knowing about the DATA Which terms best represent the data? –The mean and median best illustrate skewed data –While variance and standard deviation represent symmetrical data –Spread – how far away from the mean does the data stretch –To calculate variances – we need to square the differences between the mean and each data value. –Variance (s 2 ) - a measure of how far a set of numbers is spread out. A variance of zero indicates that all the values are identical A small variance indicates a small spread, while a large variance means the numbers are spread out Standard Deviation (s) - shows how much variation or dispersion from the average exists

20. Example: A person’s metabolic rate is the rate at which the body consumes energy. Metabolic rate is important in studies of weight gain, dieting and exercise. Here are the metabolic rate of 7 men who took part in a study of dieting (units per 24 hours) Data: 1792 1666 1362 1614 1460 1867 1439 Calculating standard deviation and variance on the calculator Use 1VAR Stats S = 189.240 calories S 2 = 35,811.667