Paper 1 (Higher tier)

State the stages of the statistical enquiry cycle.

Explain one problem of using an online survey to find out about the internet use of older people.

A town has the following numbers of adult residents (data are illustrative, written for this paper): Under 25: 240 | 25–44: 360 | 45–64: 300 | 65+: 100. A stratified sample of 50 residents is taken. Calculate how many residents aged 25–44 should be in the sample.

Explain the difference between a census and a sample survey, and give one reason for using a sample.

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

d (km)	Frequency
0 < d (km) ≤ 5	14
5 < d (km) ≤ 10	26
10 < d (km) ≤ 20	30
20 < d (km) ≤ 30	18
30 < d (km) ≤ 50	12

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.

The ages (months) of fifteen vehicles in a fleet are (data are illustrative, written for this paper): 3, 5, 6, 8, 9, 10, 12, 14, 15, 17, 19, 21, 22, 24, 41. 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.

Goals scored by a team in six matches (data are illustrative, written for this paper): 2, 4, 4, 5, 7, 8. Calculate the mean and the standard deviation. (Use σ = √(Σ(x − x̄)²/n).)

Rankings of eight countries by GDP per head and life expectancy. (data are illustrative, written for this paper)

Item	A	B	C	D	E	F	G	H
Rank 1	1	2	3	4	5	6	7	8
Rank 2	2	1	3	5	4	8	6	7

Calculate Spearman's rank correlation coefficient and interpret it.

The equation of the regression line of sales (£000) on advertising spend (£000) is y = 2.8x + 35 (data are illustrative, written for this paper). Estimate sales (£000) when advertising spend (£000) is 12.

Interpret the gradient of the regression line in context.

The data used had advertising spend (£000) values from 0 to 20. Explain why using the line to estimate sales (£000) when advertising spend (£000) is 60 may be unreliable.

Monthly visitors (hundreds) to a museum (data are illustrative, written for this paper): 12, 18, 15, 13, 19, 16, 14, 20, 17. Calculate the first two 3-point moving averages and describe the trend.

The price of a cinema ticket was £8.00 in 2019 and £10.40 in 2025. Calculate the index number for 2025 using 2019 as base year.

A quality assurance chart shows the mean weight of samples of cereal boxes. Target 500 g, warning limits 495 g and 505 g, action limits 490 g and 510 g. A sample mean is 506 g. State what action should be taken and why.

The probability that a student passes a theory test is 0.7. If a student passes a theory test, the probability that they pass the practical is 0.8; otherwise it is 0.5. Calculate the probability that they pass the practical.

Given that they pass the practical, calculate the probability that a student passes a theory test.

Events A and B are independent. P(A) = 0.4 and P(B) = 0.35. Calculate P(A and B) and P(A or B).

A basketball player scores 70% of free throws. She takes 6 free throws. The number of successes X follows a binomial distribution B(6, 0.7). Calculate P(X = 5).

The lifetimes of light bulbs (hours) are normally distributed with mean 1200 and standard deviation 100 (data are illustrative, written for this paper). Use the fact that about 68% of values lie within 1 standard deviation of the mean, and about 95% within 2, to estimate the percentage between 1000 and 1400.

A council claims that a new cycle lane has reduced traffic on a road. Describe how you would test this claim and how you would present and analyse the data.

For the last two Quarter 4 periods, actual sales were 210 and 228 and the trend values were 186.5 and 195.25 (data are illustrative, written for this paper). The trend line gives 204.0 for next year's Quarter 4. Estimate next year's Quarter 4 sales.

The table shows how 200 students travel to school (data are illustrative, written for this paper):

	Walk	Bus	Car
Year 10	35	42	23
Year 11	28	47	25

A student is chosen at random. Find (i) P(Year 11); (ii) P(Bus | Year 11); (iii) P(Year 10 | Walk).

Two groups recorded hours of exercise per week. Group A: 25 people, mean 3.2. Group B: 15 people, mean 4.8. Calculate the mean of the combined group.

In a survey of 160 people, 45 chose rugby (data are illustrative, written for this paper). Calculate the angle for rugby on a pie chart.

A spinner lands on blue with probability 0.15. Calculate the expected number of times in 400 trials (probability 0.15).

Raw data from a survey of students' ages and hours of sleep (data are illustrative, written for this paper): (15, 8), (16, 7.5), (14, 9), (61, 7), (15, 28), (16, 8.5). Identify two values that should be checked or removed when cleaning the data, giving reasons.