1. COMPUTATIONAL FORMULAS AND IQR’S

2. Compare the following heights in inches: BoysGirls 7261 7464 7065 6866 6968 7067 6865 6963 6762 7065 7166 67 64 66

3. Objective Calculate standard deviation, variance and IQR.

4. Relevance To be able to analyze a set of data and see how far each value is above or below the mean of the set.

5. Computational Formula This is an easier computational formula that contains no rounding.

6. Example – Find Var and St Dev 7 8 22 34 42

7. You Try One! 4 8 12 18 22 34 38

8. Is the standard deviation affected by outliers? 5 7 5 8 9 5 7 5 8 29

9. The standard deviation IS sensitive to extreme values.

10. 67 65 68 70 74 60 61 64 67 68 The following data represents the heights of some students in my class. a.Find the mean & standard deviation. b.What % are within 1 standard deviation of the mean? ( ) c.What % are within 2 standard deviations f the mean? (  )          

11. IQR – Interquartile Range This is the measure of variability that is not affected by outliers. It is based on quartiles.

12. 25% - This is the median of the lower ½ of the sample. - This is the median. - This is the median of the upper ½ of the sample.

13. 18242527 29303334 ) ) ( ( Q1 = 24.5Q3 = 31.5 IQR = 31.5 – 24.5 = 7

14. Find IQR 1213161822242740 Q1 = 14.5 Q3 = 25.5 IQR = 25.5 – 14.5 = 11

15. Find IQR 8101114162022262832 IQR = 15

16. Find IQR 456671022 IQR = 15

17. If normal distribution – then you can estimate the standard deviation with the IQR. *Can also be use to check to see if a distribution is normal – if much larger then it’s skewed.

18. Which Measure Should You Report? ShapeCentral Tendency Dispersion (Spread) SymmetricMeanStandard Deviation Skewed Left or Right MedianIQR NOTE: When told to “describe the distribution” you will give the shape, the center and the spread of the distribution using the above categories as a guideline.

19. Homework Worksheet Use the new formula to compute the standard deviation. Now – time for the lab!