Sample surveys: practice problems
A sample survey studies part of a group (the sample) to estimate properties of the whole group (the population).
Basic, Standard, Advanced: Grade 9 · Term 3
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Census or sample
A full survey (census) studies every member; a sample survey studies some and estimates the rest. Health check-ups need every result, while testing light bulbs would destroy them all, so a sample is used. The number of members in the sample is the sample size.
Random sampling
Samples must be chosen at random (random number dice or tables, computers, drawing lots) so that they are not biased. Volunteers only, or one class only, give biased samples.
Estimating
Assume the proportion in the sample is about the same as in the population. If 50 fish are marked and later 4 of 40 caught fish are marked, then , so there are about 500 fish.
Estimates are approximate, so answer with "about". Larger samples tend to give better estimates.
Worked examples
Which is the best way to choose a sample from all the students in a school?
- ASurvey only the students in your own class.
- BSurvey only members of sports clubs.
- CWrite every student’s name on a card, shuffle well and survey the students drawn by lot.
- DSurvey only volunteers.
Hint
The sample must be chosen at random so that it is not biased.
Answer
Solution
Choose the method in which every student is equally likely to be chosen (random sampling).
To estimate the number of fish in a pond, 50 fish are caught, marked and released. A few days later 50 fish are caught and 10 of them are marked. About how many fish are in the pond?
Hint
The proportion of marked fish in the second catch is about the same as in the whole pond.
Answer
Solution
Let the pond have fish:
Solving,
Of 798 junior high students in a city, 40 are chosen at random and 8 say they watch videos on a smartphone every day. Estimate how many of all the students do so, rounded to the nearest ten.
Hint
Apply the sample proportion to the population, then round to the nearest ten.
Answer
Solution
Using the same proportion as the sample,
Rounding to the nearest ten,
Practice problems
From all 740 students of a school, 100 were chosen at random and asked about their favourite subjects. Answer the following.
- (1)the size of the population
- (2)the size of the sample
Hint
The whole group being studied is the population; the part actually surveyed is the sample. Their sizes are the numbers of members.
Answer
- (1)
- (2)
Solution
The population is all the students; the sample is the students chosen.
To estimate the number of fish in a pond, 120 fish are caught, marked and released. A few days later 80 fish are caught and 15 of them are marked. About how many fish are in the pond?
Hint
The proportion of marked fish in the second catch is about the same as in the whole pond.
Answer
Solution
Let the pond have fish:
Solving,
Of 353 junior high students in a city, 50 are chosen at random and 34 say they watch videos on a smartphone every day. Estimate how many of all the students do so, rounded to the nearest ten.
Hint
Apply the sample proportion to the population, then round to the nearest ten.
Answer
Solution
Using the same proportion as the sample,
Rounding to the nearest ten,