Statistics worksheet — GCSE Higher

1.The masses, m kg, of 160 fish caught by a trawler in one day are grouped into classes of unequal width: 0 ≤ m < 10, 40 fish; 10 ≤ m < 30, 60 fish; 30 ≤ m < 45, 30 fish; 45 ≤ m < 50, 30 fish. A histogram is to be drawn from this table. Which set of frequency densities, listed in the same order as the classes above, is correct?

2.A scatter graph has 50 points. Most of them lie close to a rising line of best fit, but two of them lie a long way from that line. Write down how those two points should be treated.

3.A vet records the masses, m kg, of the dogs seen in one week as a histogram. The bar for 0 ≤ m < 5 has a frequency density of 4 per kg, the bar for 5 ≤ m < 15 has a frequency density of 2.6 per kg, and the bar for 15 ≤ m < 40 has a frequency density of 1.2 per kg. Work out the total number of dogs seen that week.

4.A scatter graph shows the number of days, x, that each of 16 tomato plants was watered and its height, y cm. The line of best fit has equation y = 1.5x + 4. Write down what the 1.5 in this equation tells you about the plants.

5.A cumulative frequency graph for the diameters, d mm, of 320 ball bearings is plotted from these points (upper class boundary, cumulative frequency): (10, 30), (20, 90), (30, 190), (40, 280), (50, 320). Estimate the diameter below which 90% of the ball bearings measure.

6.The mean of five test scores is 68. Four of the scores are 55, 62, 74 and 80. Work out the fifth score.

7.A charity shop in Leicester made £2,400 in one month. A pie chart shows how this was spent: repairs took up an angle of 90°, wages took up an angle of 150°, and the rest was other costs. Work out how much was spent on wages.

8.A two-way table records whether each of 50 pupils in Year 10 or Year 11 at a school walks to school or is driven. 28 of the 50 pupils are in Year 10. In total, 22 of the 50 pupils walk to school. Of the Year 10 pupils, 15 walk to school. Work out how many Year 11 pupils are driven to school.

9.A recruitment agency in Manchester compares the weekly pay, in pounds, of seven employees at two branches. Branch A: £480, £495, £500, £505, £510, £515, £1,200. Branch B: £480, £490, £500, £510, £520, £530, £540. An advert for the agency claims 'Branch A pays more on average.' Decide whether this claim is fairly supported, using an appropriate average, and choose the correct conclusion.

10.The numbers 2, 4, 6, 8, 10 and 12 have a mean of 7 and a median of 7. The value 100 is now added to the list. Which measure is changed more by adding 100, and why?

11.A town council wants to find out about the eating habits of the people who live in the town. It asks only the members of a local sports club. Give a reason why this sample is biased.

12.A factory makes a batch of 4,000 circuit boards. It checks a random sample of 50 boards and finds that 4 are faulty. The factory will scrap the whole batch if the estimated number of faulty boards in the batch is more than 250. Should the factory scrap the batch?

13.The times, t minutes, of 80 journeys are summarised by these cumulative frequencies: t < 10, 8 journeys; t < 20, 28 journeys; t < 30, 52 journeys; t < 40, 72 journeys; t < 50, 80 journeys. Estimate the interquartile range.

14.A call centre records the length, t seconds, of 100 calls: 0 ≤ t < 20, 15 calls; 20 ≤ t < 30, 24 calls; 30 ≤ t < 50, 40 calls; 50 ≤ t < 80, 21 calls. The manager's target is for a call to be finished in under 35 seconds. Estimate the number of calls that met the target.

15.In a histogram of the lengths, x cm, of some rods, the bar for 10 ≤ x < 30 has a frequency density of 3 per cm. The bar for 30 ≤ x < 45 is twice as tall as the bar for 10 ≤ x < 30. Work out the number of rods with a length in the class 30 ≤ x < 45.