Grade 7 Statistics: Random Sampling

Understand random samples

What You'll Learn

Use a random sample to estimate a population
Use several samples to see how estimates vary

📖Sampling

A random sample gives everyone the same chance to be chosen, so it tends to represent the whole population (asking only the soccer team about favorite sports would be biased). Scale the sample up: if 12 of 40 pick soccer, about 12/40 of the whole school does. Different random samples give slightly different estimates.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
Three random samples of 25 students were taken from the 750 students at a school. The number in each sample who wear glasses: 3, 8, 4. Each sample gives its own estimate for the whole school. What is the difference between the largest and smallest estimates?
1. Each sample of 25 stands for 750 ÷ 25 = 30 times as many students.
2. The estimates are 3 × 30 = 90, 8 × 30 = 240, 4 × 30 = 120. Random samples vary, so their estimates vary too.
3. Largest − smallest: 240 − 90 = 150.
Answer: 150
Example 2
Five random samples of 10 students each were taken from the 100 students at a school. The number in each sample who walk to school: 3, 2, 4, 6, 5. Use the mean of the samples to estimate how many of the 100 students walk to school.
1. Find the mean of the samples: (3 + 2 + 4 + 6 + 5) ÷ 5 = 20 ÷ 5 = 4.
2. So a typical sample of 10 has 4 who walk to school. Each sample of 10 stands for 100 ÷ 10 = 10 times as many students.
3. 4 × 10 = 40, so about 40 of the 100 students walk to school.
Answer: 40
Example 3
A random sample of 50 of the 750 students at a middle school was asked their favorite sport. Results: soccer 3, basketball 14, baseball 8 and tennis 25. Based on the sample, estimate how many of all 750 would pick basketball.
1. In the sample, 14 of the 50 chose basketball — that is 14/50 of the sample.
2. A random sample represents the whole group, so about 14/50 of all 750 chose basketball. Each person in the sample stands for 750 ÷ 50 = 15 people.
3. 14 × 15 = 210, so about 210 of the 750 would pick basketball.
Answer: 210