Statistics worksheet — GCSE Higher

1.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.

2.A histogram is drawn for the masses, m grams, of 200 letters. The bar for 0 ≤ m < 50 has a frequency density of 1.2 per gram and the bar for 50 ≤ m < 100 has a frequency density of 1.8 per gram. All the remaining letters lie in the class 100 ≤ m < 200. Work out the frequency density of the bar for 100 ≤ m < 200.

3.In a scatter graph of the age, in years, and the wingspan, in cm, of 20 birds of the same species, all the points lie close to a rising line of best fit except one, which lies a long way below the line. That bird was later found to have a damaged wing. Give a reason why this point should not be used when drawing the line of best fit.

4.A garden centre records the heights, in cm, of eleven seedlings. In order, the heights are 5, 9, x, 17, 20, 24, 28, 31, 35, 40, 44, where x is unknown. The interquartile range of the eleven heights is 19 cm. Work out the value of x.

5.In a histogram of the distances, d metres, thrown by some athletes, the bar covering 20 ≤ d < 60 has a constant frequency density of 1.8 per metre. Estimate the number of throws of at least 20 metres but less than 35 metres.

6.A café owner in Brighton records the midday temperature, x °C, and the number of hot chocolates sold, y, on 12 days. The temperatures recorded run from 4 °C to 18 °C, and the line of best fit is y = −3x + 74. The forecast for tomorrow gives a midday temperature of 12 °C. Work out the number the line of best fit predicts, and write down how much confidence the owner can have in it.

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

8.A café in York counts the number of customers in each of the nine hours it is open on one day: 4, 4, 4, 11, 13, 15, 18, 22 and 25. The owner says that a typical hour has about 4 customers, because 4 is the mode. Is the owner right? Give a reason for your answer.

9.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.

10.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.

11.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.

12.A study found that people who drink more coffee tend to concentrate better at work. A coffee company says that this shows that drinking coffee improves concentration. Give the reason why this conclusion cannot be drawn.

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

14.A Year 10 class has 20 boys with a mean height of 150 cm and 10 girls with a mean height of 168 cm. Work out the mean height of all 30 pupils in the class.

15.A council in Leeds wants to know what local people think about letting shops stay open later in the evening. It rings landline telephone numbers between 10 am and 2 pm on a Tuesday. Write down which group is most likely to be under-represented in the sample, and give a reason for your answer.