Unit 18 Measures of Variation Cumulative Frequency

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

Age in Years 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

Unit 18 Measures of Variation Cumulative Frequency 2

The table shows the distribution of marks on a test for 70 students. MarkFrequency Cumulative Frequency 1 – – – – – – – –

Marks MarkFrequency Cumulative Frequency 1 – – – – – – – – 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

Unit 18 Measures of Variation Box and Whisker Plots

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 Smallest ValueLargest Value Median Lower quartileUpper quartile Construct an additional box and whisker plot for a team with data Compare the two sets of data Construct an additional box and whisker plot for a team with data Compare the two sets of data

Unit 18 Measures of Variation Standard Deviation

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: TOTAL10 m = 8

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