1. Unit 18 Measures of Variation Cumulative Frequency

2. The table shows the age distribution (in complete years) of the population of Nigeria in 1991. Age0 ≤ x < 1515 ≤ x < 3030 ≤ x < 4545 ≤ x < 6060 ≤ x < 7575 ≤ x < 100 % of Pop.3229201261 Cumulative % 3261819399100

3. 0 10 20 30 40 50 60 70 80 90 100 Age in Years 100 90 80 70 60 50 40 30 20 10 Lower Quartile ≈ 11 Median ≈ 24 Upper Quartile ≈ 40∙5 Estimate: a)The lower quartile b)The median c)The upper quartile Estimate: a)The lower quartile b)The median c)The upper quartile

4. Unit 18 Measures of Variation Cumulative Frequency 2

5. The table shows the distribution of marks on a test for 70 students. MarkFrequency Cumulative Frequency 1 – 1022 11 – 2057 21 – 30916 31 – 4014 41 – 5016 51 – 6012 61 – 708 71 – 804 30 46 58 66 70

6. 0 10 20 30 40 50 60 70 80 Marks 80 70 60 50 40 30 20 10 MarkFrequency Cumulative Frequency 1 – 1022 11 – 2057 21 – 30916 31 – 401430 41 – 501646 51 – 601258 61 – 70866 71 – 80470 a) Draw a cumulative frequency curve b)The pass mark for the test is 47. Use your graph to determine the number of students who passed the test c)What is the probability that a student chosen at random, had a mark of less than or equal to 30? Students Pass: 70 – 42 = 28

7. Unit 18 Measures of Variation Box and Whisker Plots

8. The goals scored in the first 11 football matches played by a National Premier League team were: This data can be represented using a box and whisker plot. Record the data starting with the smallest Identify: Construct a box and whisker plot 1 0 4 2 2 3 1 2 5 0 1 0 0 1 1 1 2 2 2 3 4 5 Smallest ValueLargest Value Median Lower quartileUpper quartile 0 2 1 5 3 0 1 2 3 4 5 6 7 Construct an additional box and whisker plot for a team with data 3 5 2 1 3 3 2 5 6 2 1 Compare the two sets of data Construct an additional box and whisker plot for a team with data 3 5 2 1 3 3 2 5 6 2 1 Compare the two sets of data

9. Unit 18 Measures of Variation Standard Deviation

10. The STANDARD DEVIATION (s.d.) of a set of data is a measure of the spread of the data about the mean and is defined by a)What is the mean (m) of each set? S 1 = {6, 7, 8, 9, 10} S 2 = {4, 5, 8, 11, 12} S 3 = {1, 2, 8, 14, 15} b)The standard deviation for S 1 is calculated as: 6- 24 7- 11 800 911 1024 TOTAL10 m = 8

11. The STANDARD DEVIATION (s.d.) of a set of data is a measure of the spread of the data about the mean and is defined by S 1 = {6, 7, 8, 9, 10}m = 8 S 2 = {4, 5, 8, 11, 12}m = 8 S 3 = {1, 2, 8, 14, 15}m = 8 c)Compare the standard deviations for S 1, S 2 and S 3 S 1 = {6, 7, 8, 9, 10}s.d. ≈ 1∙414 S 2 = {4, 5, 8, 11, 12}s.d. ≈ 3∙162 S 3 = {1, 2, 8, 14, 15}s.d. ≈ 5∙831