Paper 1 (Higher tier)

Which one of the following is continuous data?

Give one advantage and one disadvantage of using secondary data.

A school has the following numbers of students (data are illustrative, written for this paper): Year 7: 180 | Year 8: 200 | Year 9: 170 | Year 10: 150 | Year 11: 100. A stratified sample of 80 students is taken. Calculate how many students from Year 9 should be in the sample.

Ecologists catch and tag 40 fish in a lake. A week later they catch 50 fish, of which 8 are tagged. Use the Petersen capture–recapture method to estimate the population.

State one assumption made in using this method.

A survey contains the question: 'Don't you agree that the canteen food is too expensive?' Give two criticisms of this question.

Write an improved question with response boxes.

State one reason for carrying out a pilot study.

The table shows (data are illustrative, written for this paper):

t (minutes)	Frequency
0 < t (minutes) ≤ 10	5
10 < t (minutes) ≤ 20	12
20 < t (minutes) ≤ 30	18
30 < t (minutes) ≤ 40	10
40 < t (minutes) ≤ 60	5

Calculate an estimate of the mean.

Explain why your answer to (a) is an estimate.

Calculate the frequency density for each class, ready to draw a histogram, and state which class has the greatest frequency density.

Use linear interpolation to estimate the median.

Estimate the 90th percentile.

Eleven students' journey times in minutes are (data are illustrative, written for this paper): 12, 15, 17, 18, 20, 21, 23, 25, 28, 30, 52. Find the median and the interquartile range.

An outlier is a value more than 1.5 × IQR below Q1 or above Q3. Show whether there are any outliers.

The number of books read by five students in a term (data are illustrative, written for this paper): 4, 7, 9, 10, 15. Calculate the mean and the standard deviation. (Use σ = √(Σ(x − x̄)²/n).)

A distribution has mean 25.1, median 23.8 and standard deviation 11.6. Calculate Pearson's coefficient of skewness, 3(mean − median) ÷ standard deviation, and describe the skew.

The product moment correlation coefficient between hours of revision and test score is 0.86. Interpret this value and state why it does not prove that revision causes higher scores.

Two judges ranked six cakes in a competition. (data are illustrative, written for this paper)

Item	A	B	C	D	E	F
Rank 1	1	2	3	4	5	6
Rank 2	2	1	4	3	6	5

Calculate Spearman's rank correlation coefficient and interpret it.

The equation of the regression line of ice creams sold on temperature (°C) is y = 3.2x + 14 (data are illustrative, written for this paper). Estimate ice creams sold when temperature (°C) is 8.

Interpret the gradient of the regression line in context.

The data used had temperature (°C) values from 0 to 30. Explain why using the line to estimate ice creams sold when temperature (°C) is 90 may be unreliable.

Quarterly sales (£000) for two years (data are illustrative, written for this paper): 40, 55, 70, 35, 44, 59, 74, 39. Calculate the first two 4-point moving averages and describe the trend.

The price of a loaf of bread was £2.40 in 2020 and £2.88 in 2024. Calculate the index number for 2024 using 2020 as base year.

A price was £50 in year 1, £54 in year 2 and £59.40 in year 3. Calculate chain base index numbers for years 2 and 3.

The probability that it rains is 0.3. If it rains, the probability that a bus is late is 0.4; otherwise it is 0.1. Calculate the probability that a bus is late.

Given that a bus is late, calculate the probability that it rains.

20% of seeds fail to germinate. Ten seeds are planted. The number of seeds that fail to germinate, X, follows a binomial distribution B(10, 0.2). Calculate P(X = 2).

A student wants to investigate whether people in towns use public transport more than people in villages. Describe how they could plan and carry out this investigation.

For the last two Quarter 4 periods, actual sales were 62 and 66 and the trend values were 51.5 and 53.5 (data are illustrative, written for this paper). The trend line gives 57.0 for next year's Quarter 4. Estimate next year's Quarter 4 sales.

Two classes sat the same test. Group A: 18 people, mean 64.5. Group B: 12 people, mean 71.0. Calculate the mean of the combined group.

In a survey of 120 people, 27 chose cycling (data are illustrative, written for this paper). Calculate the angle for cycling on a pie chart.

A biased coin lands on heads with probability 0.62. Calculate the expected number of times in 250 trials (probability 0.62).