Measures of variability

High School Topic

1. Measures of Variability

2. What are the measures of variability ? Variability- refers to the spread of scores in the distribution Range Variance Standard Deviation

3. range the difference between the highest value and the smallest value in the set Example: Given the following sorted data, find the range. 12, 15,19,24,24,25,26,30,35,38 R=HV-LV R=38-12 R=26

4. Variance Variance- it is the square of the standard deviation Note: The larger the variance, the greater the variability or the distance of scores from the mean. The smaller the variance, the lesser the variability.

5. Variance of a sample Where: = sum of the squared deviations from the mean n = total number of classes  

6. Standard deviation Used to describe variability when the mean is used to describe the central tendency Note: The mean is an average of the scores in a set while the standard deviation is a sort of average of how distant the individual scores are from the mean

7. The formula for the standard deviation Where - deviation from the mean X – the original raw score mean n – total number of observation/cases  

8. Example: Scores in a 25 item Mathematics test 23 21 19 18 18 7 15 12 10 10 8 7

9. answer n = 12 = 14 s = 5.7  

10. Quiz #1

11. The following are the response times in seconds of a smoke alarm after release of smoke from a fixed source. Find the range, variance, and standard deviation. 12 16 12 14 19 20 10 9 15

12. 2. Twenty employees of a fast food chain, give a course in first aid, obtained these scores on a test administered after the course. Find the range, variance, and standard deviation. 10 11 12 15 16 18 17 17 19 12 14 17 19 17 18 16 15 14 12 10

13. 3 . The following are the stopping distances, for 20 drivers at 30 miles per hour. Find the range, variance, and standard deviation. 69 67 56 58 70 55 70 58 70 75 72 68 80 74 61 70 61 65 58 61

14. Coefficient of relative variation (crv)’ - expressed in percentage (%) Uses of CRV: For comparing distributions measured in the same units but which have very different means For comparing distributions measured using different units

15. The formula used in cRV Where s = standard deviation = mean Note: the final answer is always expressed in percent form  

16. Example The weight of the girls in Grade 8 students are as follows. Find CRV. 37 40 47 30 37 20 48 48 49 50 36 35 28 39

17. Measures of relative standing or position

18. Measures of position/relative standing Determines the position of a single value in relation to other values in a sample or population data set

19. 4 measures of position Quartile Interquartile Percentile Z-score

20. quartile Divides a ranked data set into four equal parts 3 measures in the quartile: First quartile ( ) Second quartile ( ) Third quartile ( )  

21. First quartile Lower quartile 25% of the data (lower 25%)

22. Second quartile Median Quartile 50% of the data falls on  

23. Third quartile Upper Quartile or the upper 75%

24. example Given the following set of measurements of the grade point average of a Biology class during the second grading period. Find the quartiles 1.5 1.8 2.1 2.4 2.9 1.2 1.9 2.1 2.5 3 1.5 1.9 2.2 2.8 3 1.5 2 2.3 2.8 3.1

25. Z-score Measures the relative standing of a particular measurement in a data set.

26. Sample z-score