Grade 7 Statistics: Making Inferences

Draw conclusions from data

What You'll Learn

Estimate a population mean or count from a random sample
Compare two populations using sample means

📖Inferences

A random sample stands in for the whole population: its mean estimates the population mean, and the fraction of the sample with a trait estimates the fraction of the population. Comparing two samples' means lets you infer how the two populations differ.

Worked examples

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

Example 1
Random samples of jump-rope jumps in one minute — Team Red: 68, 67, 68, 69, 58; Team Blue: 30, 20, 23, 26, 26. Using the sample means, about how many more jumps does a typical Team Red player make than a typical Team Blue player?
1. Mean of Team Red: (68 + 67 + 68 + 69 + 58) ÷ 5 = 330 ÷ 5 = 66.
2. Mean of Team Blue: (30 + 20 + 23 + 26 + 26) ÷ 5 = 125 ÷ 5 = 25.
3. The samples are random, so their means estimate each whole group. 66 − 25 = 41, so the answer is about 41 more jumps.
Answer: 41
Example 2
A random sample of 10 of the 500 families in a town reported miles driven to work each day: 52, 15, 56, 29, 41, 40, 54, 42, 27, 29. Predict how many of all 500 drive more than 30 miles.
1. In the sample, the values more than 30 are 52, 56, 41, 40, 54, 42 — 6 of the 10.
2. The sample is random, so about 6/10 of all 500 do too. Each one in the sample stands for 500 ÷ 10 = 50.
3. 6 × 50 = 300, so about 300 of the 500 drive more than 30 miles.
Answer: 300
Example 3
Random samples of hours of sleep on a school night — Sixth graders: 10, 8, 10, 11, 11; Eighth graders: 8, 6, 6, 9, 6. Using the sample means, about how many more hours of sleep does a typical sixth grader get than a typical eighth grader?
1. Mean of Sixth graders: (10 + 8 + 10 + 11 + 11) ÷ 5 = 50 ÷ 5 = 10.
2. Mean of Eighth graders: (8 + 6 + 6 + 9 + 6) ÷ 5 = 35 ÷ 5 = 7.
3. The samples are random, so their means estimate each whole group. 10 − 7 = 3, so the answer is about 3 more hours of sleep.
Answer: 3