Processing, representing and analysing data

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.

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.

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.

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

h (cm)	Frequency
140 < h (cm) ≤ 150	6
150 < h (cm) ≤ 155	14
155 < h (cm) ≤ 160	20
160 < h (cm) ≤ 165	16
165 < h (cm) ≤ 180	9

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 marks in a test are (data are illustrative, written for this paper): 42, 45, 47, 48, 50, 51, 52, 53, 55, 56, 59. 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.

Five daily temperatures (°C) (data are illustrative, written for this paper): 10, 12, 15, 17, 21. Calculate the mean and the standard deviation. (Use σ = √(Σ(x − x̄)²/n).)

A distribution has mean 32.4, median 30.0 and standard deviation 6.0. Calculate Pearson's coefficient of skewness, 3(mean − median) ÷ standard deviation, and describe the skew.

A weighted index is calculated for a family's shopping (data are illustrative, written for this paper). Rent: index 108, weight 5; Food: index 115, weight 3; Transport: index 120, weight 2. Calculate the weighted index number.

Death rates per 1,000 in Seaview and a standard population (data are illustrative, written for this paper):

Age	Rate per 1,000	Standard population
0–29	0.8	40%
30–59	4	40%
60+	35	20%

Calculate the standardised death rate for Seaview.

Explain why a histogram rather than a bar chart is used for grouped continuous data with unequal class widths.

A scatter diagram of age of car (years) against value (£) shows strong negative correlation. Explain what this means and suggest one reason why the relationship may not be linear for very old cars.

Sales of ice cream for three years show a regular pattern: high in summer, low in winter. Explain how to use moving averages and a trend line to predict sales for next summer.

For the last two Quarter 4 periods, actual sales were 96 and 104 and the trend values were 81.5 and 86.0 (data are illustrative, written for this paper). The trend line gives 90.25 for next year's Quarter 4. Estimate next year's Quarter 4 sales.

Two branches recorded daily customer waiting times (minutes). Group A: 40 people, mean 12.5. Group B: 60 people, mean 15.0. Calculate the mean of the combined group.

In a survey of 132 people, 33 chose comedy (data are illustrative, written for this paper). Calculate the angle for comedy on a pie chart.

Two population pyramids are described (data are illustrative, written for this paper). Country X: wide base narrowing sharply with age. Country Y: narrow base, bulge at ages 40–60, many people over 70. Compare the populations and suggest one implication for Country Y.