Statistics worksheet — GCSE Higher

1.A histogram shows the speeds, v mph, of 100 vehicles passing a checkpoint. The bar for 0 ≤ v < 20 has a frequency density of 1 vehicle per mph, the bar for 20 ≤ v < 30 has a frequency density of 3 vehicles per mph, the bar for 30 ≤ v < 50 has a frequency density of 2 vehicles per mph, and the bar for 50 ≤ v < 70 has a frequency density of 0.5 vehicles per mph. Estimate the mean speed of the vehicles.

2.The masses, m kg, of 80 sacks of grain are summarised by these cumulative frequencies: m < 10, 6 sacks; m < 20, 22 sacks; m < 30, 58 sacks; m < 40, 74 sacks; m < 50, 80 sacks. Use interpolation to estimate the median mass.

3.A scatter graph shows the mass, x kg, of a parcel and the cost, y pounds, of posting it. The line of best fit is y = 1.5x + 2. Work out the estimated cost of posting a parcel with a mass of 6 kg, using the line of best fit.

4.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.

5.Write down the statement that correctly describes the difference between correlation and causation.

6.A gym in Cardiff has a scatter graph of the number of training sessions, x, attended by each member and the weight lost, y kg. The line of best fit is y = 0.4x + 1. Members want to lose at least 9 kg. Using the line of best fit, work out the least whole number of sessions needed to reach this target.

7.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.

8.A teacher records the number of pets owned by each of 25 pupils in a class; each pupil owns 0, 1, 2, 3 or 4 pets. The teacher wants to show how many pupils own each number of pets. Write down the most suitable type of chart for this data, and give a reason for your answer.

9.A survey of 25 pupils in Derby records how many siblings each has: 0 siblings — 6 pupils, 1 sibling — 10 pupils, 2 siblings — 6 pupils, 3 siblings — 3 pupils. Calculate the mean number of siblings.

10.The midday temperature in Leeds was recorded on each day of one week: 22 °C, 24 °C, 23 °C, 25 °C, 26 °C, 21 °C, 24 °C. Work out the mean midday temperature, giving your answer to 2 decimal places.

11.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.

12.Two classes at a school in Coventry sit the same maths test, out of 20 marks. Class A has a mean mark of 14 and a range of 6. Class B has a mean mark of 14 and a range of 14. Write a sentence comparing the two classes, using the mean and the range.

13.In a random sample of 40 pupils at a school, 6 are left-handed. The school has 900 pupils. Work out an estimate for the number of left-handed pupils in the school.

14.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.

15.Box plots summarise house prices, in thousands of pounds, in two towns. Town A: minimum 120, lower quartile 180, median 220, upper quartile 310, maximum 520. Town B: minimum 95, lower quartile 175, median 235, upper quartile 260, maximum 340. A buyer wants the town where house prices are typically higher but more consistent. Which statement is correct?