Estimating from Samples (Foundation)
Estimating from samples is the process of using results collected from a smaller sample of a population to predict or approximate a value for the whole population, such as a total, a proportion or a mean. This works because a well-chosen, representative sample should reflect the same patterns as the population it was taken from.
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify the size of the sample and the size of the whole population.
- Find the proportion (or fraction) of the sample that has the characteristic you are interested in.
- Multiply that proportion by the total population size to estimate the number in the whole population with that characteristic.
- If estimating an average, use the sample mean as a reasonable estimate of the population mean.
- State any assumptions, such as the sample being random and representative, since a biased sample gives an unreliable estimate.
- Round the estimate sensibly, since it is an approximation and not an exact value.
Worked example
A researcher takes a random sample of 40 apples from a delivery of 600 apples and finds that 6 of the sampled apples are bruised. Estimate the number of bruised apples in the whole delivery.
- Find the proportion of the sample that was bruised: 6/40 = 0.15.
- Multiply this proportion by the total number of apples in the delivery: 0.15 x 600 = 90.
- So the final answer is an estimated 90 bruised apples in the delivery of 600.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1A sample of 25 students from a school of 500 found that 5 walk to school. Estimate how many of all 500 students walk to school.Show answer
Answer: 100 students (5/25 = 0.2, then 0.2 x 500).
Q2A sample of 80 light bulbs from a batch of 2000 found 4 were faulty. Estimate the number of faulty bulbs in the whole batch.Show answer
Answer: 100 bulbs (4/80 = 0.05, then 0.05 x 2000).
Q3A survey of 30 shoppers out of 900 in a store found the mean amount spent was 18.50 pounds. What is the best estimate of the mean amount spent by all 900 shoppers?Show answer
Answer: 18.50 pounds (the sample mean is used as the estimate for the population mean).
Q4A random sample of 50 packets of crisps from a production run of 8000 found 3 were underweight. Estimate how many packets in the whole run are underweight.Show answer
Answer: 480 packets (3/50 = 0.06, then 0.06 x 8000).
Q5A garden centre sampled 45 out of 3000 trees and found 40 had survived the winter. Estimate how many of the 3000 trees survived the winter.Show answer
Answer: About 2667 trees (40/45 x 3000 = 2666.7, rounded to the nearest whole tree).
Q6A quality inspector samples 120 items from a batch of 15000 and finds 3 defective, but the sample was taken only from items made in the last hour of the day. Explain why her estimate might not be reliable, and give the estimate assuming the sample were representative.Show answer
Answer: The sample may be biased as it excludes earlier production, so may not be representative; assuming it were, estimate = 3/120 x 15000 = 375 defective items.
Exam-style questions
Written in the style of a GCSE Statistics exam paper, with a full mark scheme.
A random sample of 60 out of 1500 visitors to a theme park were asked if they had been before; 18 said yes. Estimate the number of the 1500 visitors who had been to the park before.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A farmer takes a random sample of 25 chickens from a flock of 400 and weighs them, finding a mean weight of 2.2 kg and that 4 of the 25 chickens weigh over 3 kg. Estimate (a) the mean weight of the whole flock, and (b) the number of chickens in the whole flock that weigh over 3 kg.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A council wants to estimate how many of the 12000 households in a town recycle regularly. A random sample of 150 households is surveyed and 96 say they recycle regularly. (a) Use the sample to estimate the number of households in the town that recycle regularly. (b) The council later discovers the sample was taken only from one street. Explain why this might make the estimate unreliable.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
See real GCSE Statistics past-paper questions, with official mark schemes →
Free printable worksheet
Want more practice on paper? Download the estimating from samples (foundation) worksheet pack - 15 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 2 of GCSE Statistics Foundation Workbook 1, the whole course as one free printable PDF.
Other cuts of this worksheet:
Next topics
Not quite what you needed?
Tell us what is missing on estimating from samples (foundation), or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.