A focused Grade 7 learning session for Making Inferences from Random Samples using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving making inferences from random samples.
Making Inferences from Random Samples is part of Grade 7 Statistics. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of making inferences from random samples using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Making Inferences from Random Samples, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving making inferences from random samples.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
In a random sample of \(50\) students, \(18\) said they prefer science. About how many students in the whole school of \(800\) are likely to prefer science?
Answer B: \(288\)
Set up the proportion: \(\frac{18}{50}=\frac{x}{800}\). Solve: \(x=\frac{18\times800}{50}=288\).
In a random sample of \(120\) middle school students, \(45\) play a musical instrument. The school has \(840\) students. About how many are likely to play an instrument?
Answer B: \(315\)
\(\frac{45}{120}=\frac{x}{840}\). Reduce to \(\frac{3}{8}=\frac{x}{840} \Rightarrow x = 315\).
In a sample of \(90\) items from a factory, \(27\) were defective. If the factory produces \(2700\) items per day, about how many are expected to be defective?
Answer C: \(810\)
\(\frac{27}{90}=\frac{x}{2700}\). Reduce to \(\frac{3}{10} \Rightarrow x = 810\).
A health clinic surveyed \(150\) patients and found that \(42\) have high blood pressure. The clinic sees \(500\) patients per month. About how many have high blood pressure?
Answer C: \(140\)
\(\frac{42}{150}=\frac{x}{500}\). Simplify: \(\frac{7}{25}=\frac{x}{500} \Rightarrow x = 140\).
In a sample of \(100\) apps on a phone, \(16\) are gaming apps. A mobile device company has \(8000\) app downloads tracked. About how many are gaming apps?
Answer C: \(1280\)
\(\frac{16}{100}=\frac{x}{8000}\). So \(x = 0.16 \times 8000 = 1280\).
Three samples show proportions of \(\frac{15}{50}\), \(\frac{12}{40}\), and \(\frac{18}{72}\) of students who prefer science. Which two samples have the same proportion?
Answer A: First and second
\(\frac{15}{50}=0.30\); \(\frac{12}{40}=0.30\); \(\frac{18}{72}=0.25\). First and second both equal \(30\%\).
A survey of \(70\) people found \(28\) prefer hiking. Which estimate of the total population preferring hiking is most reasonable if the population is \(3500\)?
Answer C: \(1400\)
\(\frac{28}{70}=\frac{x}{3500}\). Reduce: \(\frac{2}{5}=\frac{x}{3500} \Rightarrow x = 1400\).
In a sample of \(160\) grocery shoppers, \(64\) bought organic produce. The store has approximately \(4000\) customers per week. About how many buy organic produce?
Answer C: \(1600\)
\(\frac{64}{160}=\frac{x}{4000}\). Reduce: \(\frac{2}{5}=\frac{x}{4000} \Rightarrow x = 1600\).
A random sample of \(125\) vehicles found \(50\) were electric cars. The city has \(5000\) registered vehicles. How many are estimated to be electric?
Answer A: \(2000\)
\(\frac{50}{125}=\frac{x}{5000}\). Reduce: \(\frac{2}{5}=\frac{x}{5000} \Rightarrow x = 2000\).
Which sample shows the highest proportion of left-handed individuals?
Answer B: Sample B
Sample A: \(\frac{12}{80}=0.15\) or \(15\%\); Sample B: \(\frac{15}{75}=0.20\) or \(20\%\); Sample C: \(\frac{18}{120}=0.15\) or \(15\%\). Sample B is highest.
A poll of \(200\) voters found \(84\) support a new law. In a city of \(50000\) voters, how many are expected to support the law?
Answer C: \(21000\)
\(\frac{84}{200}=\frac{x}{50000}\). Reduce: \(\frac{21}{50}=\frac{x}{50000} \Rightarrow x = 21000\).
