Paper 2 (Higher tier)

Which sampling method selects the first people the researcher meets?

Explain the difference between a population and a sample.

Describe how to take a systematic sample of 50 from a list of 1,000 customers.

Explain what is meant by an extraneous variable, using an example from an experiment on plant growth.

Ecologists catch and tag 60 newts in a lake. A week later they catch 45 newts, of which 9 are tagged. Use the Petersen capture–recapture method to estimate the population.

State one assumption made in using this method.

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

m (kg)	Frequency
40 < m (kg) ≤ 50	8
50 < m (kg) ≤ 55	15
55 < m (kg) ≤ 60	22
60 < m (kg) ≤ 70	18
70 < m (kg) ≤ 90	7

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.

Fifteen daily rainfall totals (mm) for a month are (data are illustrative, written for this paper): 31, 34, 36, 38, 40, 41, 42, 44, 45, 47, 49, 50, 53, 55, 78. 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 scores in a quiz (data are illustrative, written for this paper): 12, 15, 18, 20, 25. Calculate the mean and the standard deviation. (Use σ = √(Σ(x − x̄)²/n).)

A distribution has mean 46.2, median 49.0 and standard deviation 8.4. Calculate Pearson's coefficient of skewness, 3(mean − median) ÷ standard deviation, and describe the skew.

Two teachers ranked seven pieces of coursework. (data are illustrative, written for this paper)

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

Calculate Spearman's rank correlation coefficient and interpret it.

The equation of the regression line of number of electric cars (thousands) on years since 2015 is y = 4.5x + 12 (data are illustrative, written for this paper). Estimate number of electric cars (thousands) when years since 2015 is 6.

Interpret the gradient of the regression line in context.

The data used had years since 2015 values from 0 to 8. Explain why using the line to estimate number of electric cars (thousands) when years since 2015 is 24 may be unreliable.

A weighted index is calculated for a family's shopping (data are illustrative, written for this paper). Bread: index 110, weight 3; Milk: index 120, weight 2; Eggs: index 105, weight 5. Calculate the weighted index number.

A town has a population of 60,000 and there were 450 deaths last year (data are illustrative, written for this paper). Calculate the crude death rate per 1,000.

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

Age	Rate per 1,000	Standard population
0–39	1.2	50%
40–64	5	30%
65+	40	20%

Calculate the standardised death rate for Town A.

Explain why standardised rates are better than crude rates for comparing towns.

In a group of 50 students, 28 study football, 22 study tennis and 9 study both (data are illustrative, written for this paper). How many study neither?

A student who studies tennis is chosen at random. Find the probability that they also study football.

The heights of adult men in a town are normally distributed with mean 170 and standard deviation 8 (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 162 and 186.

A spinner lands on red with probability 0.25. It is spun 8 times. The number of successes X follows a binomial distribution B(8, 0.25). Calculate P(X = 3).

A dice is rolled 300 times and lands on six 72 times. Compare the experimental probability with the theoretical probability and comment on fairness.

Compare the distributions of two classes' test marks: Class A median 54, IQR 12, range 40; Class B median 61, IQR 22, range 45.

Give three reasons why a pie chart would be a poor choice for showing how the temperature in a town changes over a year.

The table shows how 150 students travel to school (data are illustrative, written for this paper):

	Walk	Bus	Car
Boys	24	30	16
Girls	20	38	22

A student is chosen at random. Find (i) P(Girls); (ii) P(Bus | Girls); (iii) P(Boys | Walk).

For the last two Quarter 4 periods, actual sales were 48 and 53 and the trend values were 41.25 and 43.75 (data are illustrative, written for this paper). The trend line gives 47.5 for next year's Quarter 4. Estimate next year's Quarter 4 sales.

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.