Maths Lit Worksheet - Measures Of Central Tendency And Spread

SAEP Matric Success – Zisukhanyo Maths Lit Worksheet Tuesday 31st March 2009 Measures of central tendency and spread 1. Six boys have heights of 1,53 m; 1,49 m; 1,60 m; 1,65 m; 1,90 m and 1,43 m. a) Write down the mean height of the six boys. b) Write down the mean height of the remaining five boys when the shortest boy leaves. 2. A proofreader reads through a 250-page manuscript. The number of mistakes found on each page are summarised in the table below. Number of mistakes Number of pages

0 61

1 109

2 53

3 23

4 4

Determine the mean number of errors found per page to one decimal place. 3. Write down the median of the following sets of numbers. a) 3; 12; 4; 6; 8; 5; 4 b) 7; 21; 2; 17; 3; 13; 7; 4; 9; 7; 9 4. The heights of the Sharks rugby team during their last match were: 1,89 m; 1,9 m; 1,83 m; 1,79 m; 1,92 m; 1,88 m; 1,81 m; 2,1 m; 1,87 m; 1,93 m; 1,88 m; 1,77 m; 1,89 m; 1,85 m; 1,99 m The heights of the Cheetahs rugby team were: 1,79 m; 1,81 m; 1,83 m; 1,98 m; 1,93 m; 1,87 m; 1,80 m; 2 m; 1,89 m; 1,91 m; 1,87 m; 1,78 m; 1,89 m; 1,86 m; 1,96 m Write down the difference in their median heights. 5. Write down the mode of the following sets of numbers. a) 3; 12; 4; 6; 8; 5; 4; b) 7; 21; 2; 17; 3; 13; 7; 4; 9; 7; 9 6. A bridge player keeps a note of the number of aces that she receives in successive deals. The numbers are: 0; 2; 3; 0; 0; 2; 1; 1; 0; 2; 3; 0; 1; 1; 2; 1; 0; 0 Write down: a) the mode b) the median c) the mean of the numbers of aces she receives 7. Learners write a Maths test every Friday for two and a half months. a) Thandi’s marks out of 20 are: 2; 16; 12; 12; 18; 10; 10; 8; 4; 8. Calculate the mean and range of her marks. b) Jill’s marks out of 20 are: 10; 10; 8; 8; 14; 14; 10; 6; 8; 12. Calculate the mean and range of her marks. c) Explain who (Thandi or Jill) did better in your opinion.

8. Write down the median, lower quartile, upper quartile and inter-quartile range for the following: a) 12; 12; 15; 16; 17; 20; 21; 23; 25; 25; 27; 27 b) 8; 8; 9; 10; 11; 11; 11; 11; 14; 15 9. A garage notes the mileage of vehicles brought in for a 10 000 km service. The data is in the following table. Mileage (‘000 km) Number of vehicles

97

1018

1113

128

Write down the lower and upper quartiles and the 5th and 50th percentiles. 10. At a school, the learners were asked to fill in a form about the distance in kilometres from their homes to the school. The results are shown in the table below. a) Write down the modal class b) Calculate and estimate for mean distance c) Complete the cumulative frequency table d) Draw a cumulative frequency diagram. Use a scale of 5 cm for 5 km on the horizontal axis and 1 cm for 10 learners on the vertical axis. e) Use the graph to estimate the median distance f) Use the graph to estimate the inter-quartile range g) How many learners live less than 10 km away from the school? h) How many learners live more than 10 km away from the school? What is this percentage? Distance in km 0
Frequency (f) 50 85 68 26 9 12

Cumulative frequency 50 135

11. The times taken for a group of experienced mice to run through a maze are compared with the times for a group of inexperienced mice. a) Write down the median and the upper and lower quartiles for each group of mice b) Plot the two sets of data on a single graph using box plots c) Comment on the results Experienced mice: 121; 137; 130; 128; 132; 127; 129; 131; 135; 130; 126; 120; 118; 125 Inexperience mice: 135; 142; 145; 156; 149; 134; 139; 126; 147; 152; 153; 145; 144; 146