Maths Lit Worksheet - Statistical Measures And Diagrams
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SAEP Matric Success – Zisukhanyo Maths Lit Worksheet Tuesday 24th March 2009 Statistical measures and diagrams 1. Through the year, the weekly sales of a product at ASPA was recorded. a) Copy the table and complete the cumulative frequency column b) Draw the cumulative frequency curve by joining the cumulative frequency points by a curve. Use the upper class boundaries on the horizontal axis. Number sold 251 – 270 271 – 290 291 – 310 311 – 330 331 – 350 351 – 370 371 – 390 Total
Frequency (f) 2 5 12 16 8 6 3 52
Cumulative frequency 2 7
2. In 1996, the age distribution of the female population in South Africa (in millions) was Total 21
Under 4 2,2
5 – 14 4,6
15 – 24 4,1
25 – 34 3,4
35 – 44 2,5
45 – 59 2,2
60 – 64 0,5
65 – 74 0,8
Over 75 0,6
a) Copy and complete the table of cumulative frequencies below Age Under 4 5 – 14 15 – 24 15 – 34 35 – 44 45 – 59 60 – 64 65 – 74 Over 75
Frequency (millions) 2,2 4,6 4,1 3,4 2,5 2,2 0,5 0,8 0,6
Cumulative frequency (millions) 2,2 6,8
b) Plot the points against the upper class boundaries and draw a cumulative frequency polygon by connecting the points by straight lines.
3. For each of the scatter plots below state: i) whether there is a positive, negative or no correlation between the variables ii) whether or not the relationship appears to be linear iii) the strength of the correlation (zero, weak, moderate or strong)
4. a) Plot a scatter plot for the following sets of data. b) What does each scatter plot show? i) Maths 23 45 73 35 67 44 32 66 84 36
Science 30 41 67 74 77 50 41 55 70 32
ii) Height 162 155 158 142 146 165 171 148 150
Arm-span 160 151 157 144 148 163 167 150 147
5. Eighty South Africans were asked to predict who they think will win the 2010 World Cup Soccer finals that will be held in South Africa. Their answers were: Italy 10 Brazil 42 Portugal 16 South Africa 8 England 4 80
Work out: a) (10/80) x 360° b) (42/80) x 360° c) (16/80) x 360° d) (8/80) x 360° e) (4/80) x 360° f) Draw an accurate pie chart to display the predictions g) Do you think South Africa has a chance of winning the World Cup? If not, what made 10 respondents choose South Africa? 6. The pie chart below shows how May spends her time in a Maths lesson, which lasts 50 minutes. How much time (to the nearest minute) does she spend: a) getting ready to work? b) talking? c) sharpening a pencil? d) She spends 5 minutes working. What is the angle on the pie chart for the time spent working?
7. In a survey the heights of children aged 15 were measured in four countries around the world. A computer chose a random sample of children, not necessarily the same number from each country. Use the graphs A-D to identify the country in each of the statements.
a) Country … is poor and the diet of the children is not good. Two thirds of the children were less than 150 cm tall. b) There were 54 children in the sample from country … . c) In country …, the heights were spread fairly evenly across the range 130 to 180 cm. d) Country … is famous for producing lots of good high jumpers and basketball players. e) The smallest sample of children came from country … . f) In country … three quarters of the children were either tall or short. 8. The telephonist answers telephone calls arriving at a switchboard. The table shows the time, to the nearest second, recorded as being taken by the telephonist to answer the calls received during one day.
Time to answer (to nearest second) 10 – 19 20 – 24 25 – 29 30 31 – 34 35 – 39 40 – 59
Number of calls 20 20 15 14 16 10 10
a) Draw up a table to calculate frequency density and represent the data by a histogram b) Give a reason to justify the use of a histogram to represent these data 9. The scatter plot below shows the age and value for a sample of cars of a particular model. A line of good fit has been drawn for these points. Use the line to predict the value of a car of this model of age: a) 2 years b) 5 years c) 10 years Use the line to predict the age of a car of this model with value: d) R28 000 e) R18 000 f) R10 000
Frequency (f) 2 5 12 16 8 6 3 52
Cumulative frequency 2 7
2. In 1996, the age distribution of the female population in South Africa (in millions) was Total 21
Under 4 2,2
5 – 14 4,6
15 – 24 4,1
25 – 34 3,4
35 – 44 2,5
45 – 59 2,2
60 – 64 0,5
65 – 74 0,8
Over 75 0,6
a) Copy and complete the table of cumulative frequencies below Age Under 4 5 – 14 15 – 24 15 – 34 35 – 44 45 – 59 60 – 64 65 – 74 Over 75
Frequency (millions) 2,2 4,6 4,1 3,4 2,5 2,2 0,5 0,8 0,6
Cumulative frequency (millions) 2,2 6,8
b) Plot the points against the upper class boundaries and draw a cumulative frequency polygon by connecting the points by straight lines.
3. For each of the scatter plots below state: i) whether there is a positive, negative or no correlation between the variables ii) whether or not the relationship appears to be linear iii) the strength of the correlation (zero, weak, moderate or strong)
4. a) Plot a scatter plot for the following sets of data. b) What does each scatter plot show? i) Maths 23 45 73 35 67 44 32 66 84 36
Science 30 41 67 74 77 50 41 55 70 32
ii) Height 162 155 158 142 146 165 171 148 150
Arm-span 160 151 157 144 148 163 167 150 147
5. Eighty South Africans were asked to predict who they think will win the 2010 World Cup Soccer finals that will be held in South Africa. Their answers were: Italy 10 Brazil 42 Portugal 16 South Africa 8 England 4 80
Work out: a) (10/80) x 360° b) (42/80) x 360° c) (16/80) x 360° d) (8/80) x 360° e) (4/80) x 360° f) Draw an accurate pie chart to display the predictions g) Do you think South Africa has a chance of winning the World Cup? If not, what made 10 respondents choose South Africa? 6. The pie chart below shows how May spends her time in a Maths lesson, which lasts 50 minutes. How much time (to the nearest minute) does she spend: a) getting ready to work? b) talking? c) sharpening a pencil? d) She spends 5 minutes working. What is the angle on the pie chart for the time spent working?
7. In a survey the heights of children aged 15 were measured in four countries around the world. A computer chose a random sample of children, not necessarily the same number from each country. Use the graphs A-D to identify the country in each of the statements.
a) Country … is poor and the diet of the children is not good. Two thirds of the children were less than 150 cm tall. b) There were 54 children in the sample from country … . c) In country …, the heights were spread fairly evenly across the range 130 to 180 cm. d) Country … is famous for producing lots of good high jumpers and basketball players. e) The smallest sample of children came from country … . f) In country … three quarters of the children were either tall or short. 8. The telephonist answers telephone calls arriving at a switchboard. The table shows the time, to the nearest second, recorded as being taken by the telephonist to answer the calls received during one day.
Time to answer (to nearest second) 10 – 19 20 – 24 25 – 29 30 31 – 34 35 – 39 40 – 59
Number of calls 20 20 15 14 16 10 10
a) Draw up a table to calculate frequency density and represent the data by a histogram b) Give a reason to justify the use of a histogram to represent these data 9. The scatter plot below shows the age and value for a sample of cars of a particular model. A line of good fit has been drawn for these points. Use the line to predict the value of a car of this model of age: a) 2 years b) 5 years c) 10 years Use the line to predict the age of a car of this model with value: d) R28 000 e) R18 000 f) R10 000
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