Describing sampling methods

Questions that ask to identify, explain, or compare different sampling methods (stratified, systematic, simple random) or discuss advantages/disadvantages of sampling approaches.

6 questions

Edexcel AS Paper 2 2020 June Q4
  1. A lake contains three different types of carp.
There are an estimated 450 mirror carp, 300 leather carp and 850 common carp.
Tim wishes to investigate the health of the fish in the lake.
He decides to take a sample of 160 fish.
  1. Give a reason why stratified random sampling cannot be used.
  2. Explain how a sample of size 160 could be taken to ensure that the estimated populations of each type of carp are fairly represented. You should state the name of the sampling method used. As part of the health check, Tim weighed the fish.
    His results are given in the table below.
    Weight (wkg)Frequency (f)Midpoint (m kg)
    \(2 \leqslant w < 3.5\)82.75
    \(3.5 \leqslant w < 4\)323.75
    \(4 \leqslant w < 4.5\)644.25
    \(4.5 \leqslant w < 5\)404.75
    \(5 \leqslant w < 6\)165.5
    $$\left( \text { You may use } \sum \mathrm { f } m = 692 \quad \text { and } \quad \sum \mathrm { f } m ^ { 2 } = 3053 \right)$$
  3. Calculate an estimate for the standard deviation of the weight of the carp. Tim realised that he had transposed the figures for 2 of the weights of the fish.
    He had recorded in the table 2.3 instead of 3.2 and 4.6 instead of 6.4
  4. Without calculating a new estimate for the standard deviation, state what effect
    1. using the correct figure of 3.2 instead of 2.3
    2. using the correct figure of 6.4 instead of 4.6
      would have on your estimated standard deviation.
      Give a reason for each of your answers.
OCR PURE Q9
9 Jo is investigating the popularity of a certain band amongst students at her school. She decides to survey a sample of 100 students.
  1. State an advantage of using a stratified sample rather than a simple random sample.
  2. Explain whether it would be reasonable for Jo to use her results to draw conclusions about all students in the UK.
OCR MEI AS Paper 2 2020 November Q3
3 A researcher is conducting an investigation into the number of portions of fruit adults consume each day. The researcher decides to ask 50 men and 50 women to complete a simple questionnaire.
  1. State the type of sampling procedure the researcher is using.
  2. Write down one disadvantage of this sampling procedure. The researcher represents the data in Fig. 3.1. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Number of portions of fruit consumed by adults} \includegraphics[alt={},max width=\textwidth]{c08a2212-3104-425e-8aee-7f2d46f23924-06_531_991_701_248}
    \end{figure} Fig. 3.1
  3. Describe the shape of the distribution. The data are summarised in the frequency table in Fig. 3.2. \begin{table}[h]
    Number of portions of fruit012345
    Number of adults1834261174
    \captionsetup{labelformat=empty} \caption{Fig. 3.2}
    \end{table}
  4. For the data in Fig. 3.2, use your calculator to find
    • the mean,
    • the standard deviation.
    Give your answers correct to 2 decimal places. A second researcher chooses a proportional stratified sample of 100 children from years 5 and 6 in a certain primary school. There are 220 children to choose from. In year 5 there are 125 children, of whom 81 are boys.
  5. How many year 5 girls should be included in the sample? The second researcher found that the mean number of portions of fruit consumed per day by the children in this sample was 1.61 and the standard deviation was 0.53 .
  6. Comment on the amount of fruit consumed per day by the children compared to the amount of fruit consumed per day by the adults.
SPS SPS SM Statistics 2024 January Q3
3. Zac is planning to write a report on the music preferences of the students at his college. There is a large number of students at the college.
  1. State one reason why Zac might wish to obtain information from a sample of students, rather than from all the students.
  2. Amaya suggests that Zac should use a sample that is stratified by school year. Give one advantage of this method as compared with random sampling, in this context. Zac decides to take a random sample of 60 students from his college. He asks each student how many hours per week, on average, they spend listening to music during term. From his results he calculates the following statistics.
    Mean
    Standard
    deviation
    		Median
    Lower
    quartile
    Upper
    quartile
    21.04.2020.518.022.9
  3. Sundip tells Zac that, during term, she spends on average 30 hours per week listening to music. Discuss briefly whether this value should be considered an outlier.
  4. Layla claims that, during term, each student spends on average 20 hours per week listening to music. Zac believes that the true figure is higher than 20 hours. He uses his results to carry out a hypothesis test at the \(5 \%\) significance level. Assume that the time spent listening to music is normally distributed with standard deviation 4.20 hours. Carry out the test.
AQA Paper 3 2022 June Q15
15 Researchers are investigating the average time spent on social media by adults on the electoral register of a town. They select every 100th adult from the electoral register for their investigation.
15
  1. Identify the population in their investigation.
    15
    1. State the name of this method of sampling.
      15
  3. (ii) Describe one advantage of this sampling method.
    \includegraphics[max width=\textwidth, alt={}, center]{6ad3bac9-bf08-443d-8be2-b0c26209ffe8-23_2488_1716_219_153}
Edexcel AS Paper 2 Specimen Q1
  1. Sara is investigating the variation in daily maximum gust, \(t \mathrm { kn }\), for Camborne in June and July 1987.
She used the large data set to select a sample of size 20 from the June and July data for 1987. Sara selected the first value using a random number from 1 to 4 and then selected every third value after that.
  1. State the sampling technique Sara used.
  2. From your knowledge of the large data set explain why this process may not generate a sample of size 20 . The data Sara collected are summarised as follows $$n = 20 \quad \sum t = 374 \quad \sum t ^ { 2 } = 7600$$
  3. Calculate the standard deviation.