17 D measuring spread of data

1. 17 D measuring spread of data

2. To be able to describe a set of data we need to Measure both its 1) center and 2) its spread

3. Three distributions B and A has the same mean but different spreads

4. 4 different measures of spread • 1) range • 2)interquartile range IQR • 3) variance • 4) standard deviation

5. The range • Difference between the maximum and minmum data value

6. The interquartile range interquartile range= upper quartile – lower quartile

7. Median and the qurtiles • The median divides the data set into two halves • The quartiles you get if you divide the halfs again and take the mean of the halfs..

10. Example • Find the interquartile range for the data set • 6,4,7,5,3,4,2,6,5,7,5,3,8,9,3,6,5 • First find the median and then lower and upper quartile

11. Example • Find the interquartile range for the data set • 6,4,7,5,3,4,2,6,5,7,5,3,8,9,3,6,5 • First find the median and then lower and upper quartile • Median = 5 (nine th value)

12. 2 3 3 3 4 4 5 5 lower quartile is the mean of this sequence • Q1 = (3+4)/2 = 3.5

13. Upper half • 5 6 6 6 7 7 8 9 • Q3 = (6+7)/2 = 6.5

14. Now • The quartile range = upper quartile – lower quartile • IQR = Q3 – Q1 • IQ3 = 6.5 -3.5 = 3

15. Percentile • Is the score below which a certain percentage of the data lies.

16. The lower quartile Q1 • Is the 25 th percentile • Since 25 % of the data points are below this value

17. If you score in a test is the 85% percentile then 85% of the class has scored less than you.

18. Statistical term ogive • Also called ogee

19. Cumultative data

21. The word ogive//ogee originally come from a term in architecture for a diagonal rib of a Gothic vault or a pointed arch • the Late Latin obvita, the feminine past participle of obvire, to resist or go against (and thus supporting).

23. Looking at the 80 th percentile80% has less than 60 marks

24. Percentiles • Lower quartiel is 25 th percentile • 25 % of the data are below this data point

25. Percentiles • Lower quartile is 25 th percentile • 25 % of the data are below this data point • Median is the 50 th percentile • And upper quartile Q3 is the 75 th percentile