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1. The countries of the world are divided into ‘developed’ and ‘under-developed’ countries. The frequency table shows the distribution of ages for the population in the developed countries. The figures are percentages and were estimated for the year 1985.
|Age |Percentage of |Cumulative |
|(y years) |population |Percentage |
|0 < y ≤ 15 |19 | |
|15 < y ≤ 30 |22 | |
|30 < y ≤ 45 |20 | |
|45 < y ≤ 60 |17 | |
|60 < y ≤ 75 |11 | |
|75 < y ≤ 90 |9 | |
| 90 < y ≤ 105 |2 | |
(a) On graph paper construct a cumulative frequency diagram to show this information.
[pic]
(b) (i) What was the median age for the population in developed countries in 1985?
(ii) The median age for the population in the under-developed countries in 1985 was 21.
What do the medians tell you about the difference between the population in the developed countries and the population in the underdeveloped countries?
2. Pete wanted to find out the length of time cars were left in a car park. His results, to the nearest minute, are given in the table.
|Length of stay |Number of cars |Cumulative |
|(minutes) |(frequency) |frequency |
|0 < t ≤ 15 |0 | |
|15 < t ≤ 30 |23 | |
|30 < t ≤ 45 |35 | |
|45 < t ≤ 60 |41 | |
|60 < t ≤ 75 |63 | |
|75 < t ≤ 90 |21 | |
|90 < t ≤ 120 |10 | |
|120 < t ≤ 135 |7 | |
(a) Copy and complete the table.
(b) Draw a cumulative frequency diagram for the data.
[pic]
(c) Use your diagram to estimate the inter-quartile range.
(d) The owners of the car park think that about two thirds of the cars are parked for between 40 and 80 minutes. Do Pete’s results support this? Give a reason for your answer.
3. The lengths of a number of nails were measured to the nearest 0.01 cm, and the following frequency distribution was obtained.
[pic]
(a) Complete the cumulative frequency column.
(b) Draw a cumulative frequency diagram and use it to estimate
(i) the median length of the nails, (ii) the inter-quartile range
[pic]
4. Laura and Joy played 40 games of golf together.
The table below shows Laura’s scores.
[pic]
(a) On your graph paper draw a cumulative frequency diagram to show Laura’s scores.
[pic]
(b) Making your method clear, use your graph to find
(i) Laura’s median score,
(ii) the inter-quartile range of her scores
(c) Joy’s median score was 103.
The inter-quartile range of her scores was 6.
(i) Who was the more consistent player?
Give a reason for your choice.
(ii) The winner of a game of golf is the one with the lowest score.
Who won most of the 40 games?
Give a reason for your choice.
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5. The following data refers to the average number of paid hours worked by 5000 men and 5000 women per week in the UK in 1990.
[pic]
(a) Copy and complete the table to show the cumulative percentage frequency of the paid hours worked by men.
The graph shows the cumulative percentage frequency of the paid hours worked by women.
[pic]
(b) Copy this graph onto your graph paper , on the same grid, draw the cumulative percentage frequency graph of the paid hours worked by men.
(c) By finding the inter-quartile ranges of the two distributions, state whether men or women had the greater variability in the number of paid hours worked per week.
6. Every day James does a test to see how many units of sugar are present in his blood. The results of these tests over a period of 50 days are shown in the table below.
[pic]
(a) Copy and complete the table by filling in the cumulative frequencies.
(b) On graph paper, draw a cumulative frequency diagram.
[pic]
(c) Use your graph to find the median value of x.
(d) If the sugar content of James’ blood is greater than 11.5 units, then it is harmful to his health. Use your graph to find an estimate of the number of times these readings were greater than 11.5 units. Show clearly on your graph how you got your answer.
7. An examiner marked 320 examination papers. He noted the time it took to mark each one. The table gives a summary of these times.
[pic]
(a) (i) Complete the table by filling in the cumulative frequencies.
(ii) On the grid below draw a cumulative frequency diagram to show this information.
(b) Making your method clear, use your diagram to find
(i) the median time taken to mark each paper,
(ii) the inter-quartile range of the times taken.
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