Statistics worksheet — GCSE Higher

1.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.

2.A histogram shows the ages, in years, of 250 members of a running club. The bar for the class 10 ≤ age < 20 has a frequency density of 4.5 members per year, the bar for 20 ≤ age < 35 has a frequency density of 6 members per year, and the bar for 50 ≤ age < 70 has a frequency density of 2.75 members per year. Work out the frequency of the remaining class, 35 ≤ age < 50.

3.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.

4.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.

5.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?

6.In a histogram of the heights, h cm, of 90 seedlings, the class 12 ≤ h < 18 contains 36 seedlings. Work out the frequency density for this class.

7.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.

8.A scatter graph shows the midday temperature, x °C, and the number of ice creams sold at a seaside kiosk, y. The line of best fit is y = 3x − 20. Give a reason why the y-intercept of this line of best fit is not a sensible estimate of the number of ice creams sold.

9.A vet records the masses, m kg, of 30 dogs at a clinic in Preston: 0 < m ≤ 10 — 11 dogs, 10 < m ≤ 20 — 5 dogs, 20 < m ≤ 30 — 5 dogs, 30 < m ≤ 40 — 9 dogs. Work out an estimate for the mean mass, in kg, using the midpoint of each class interval.

10.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.

11.Priya travels to work by one of two routes and records her journey times, in minutes, over several weeks. Route 1 has a median of 34 minutes and an interquartile range of 22 minutes. Route 2 has a median of 41 minutes and an interquartile range of 6 minutes. Priya wants the more reliable route for getting to an important meeting on time. Which route should she choose, and why?

12.Four pairs of variables are listed below. Write down the pair that you would expect to show negative correlation.

13.Forty pupils in class P and forty pupils in class Q each solved a puzzle. The times, in seconds, were summarised using cumulative frequency. For class P the lower quartile is 24, the median is 38 and the upper quartile is 46. For class Q the lower quartile is 30, the median is 35 and the upper quartile is 44. Write down the statement that correctly compares the two classes.

14.A two-way table records the favourite subject, Maths or Art, of 60 pupils in Year 10, and whether each pupil is left-handed or right-handed. 9 of the 60 pupils are left-handed, and 6 of those left-handed pupils prefer Art. In total, 24 of the 60 pupils prefer Art. A pupil is chosen at random from the 60. Work out the probability that the pupil is right-handed and prefers Art.

15.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.