Skip to content
Brainsladder

Understand Statistics and Random Sampling

Students understand that statistics can be used to gain information about a population by examining a sample. They distinguish valid (random) from invalid sampling methods and understand that a larger random sample gives more reliable estimates of population characteristics.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Understand Statistics and Random Sampling

Grade 7 · Statistics and Probability · question 1 of 3

0 of 20

20 rungs. A star at the top.

A student says a sample of 500 soccer-team lockers is better than 40 lockers from a mixed school list because 500 is bigger. What went wrong?

How it is taught

0:00 of 3:52

A population is the whole group you want to know about.

A random sample gives every member a fair chance to be chosen.

Read it: A random sample

Ask the students at the first table in the lunchroom, and most students have no chance to be picked: that plan is biased. Write every student's name on a card, mix the cards and pick 25, and every student has the same chance: that plan is random.

  1. Ask of each plan: who in the group could be picked?
  2. If every member of the group could be picked, each with the same chance, the plan is random.
  3. If some members are left out, or are likelier to be picked than others, the plan is biased.

A sample stands for the whole group, so it should be like the whole group.

The students at one table may be friends who like the same things, so their answers can differ from the rest of the school's.

Mixing every name and picking by chance leaves nobody out, so the sample is likely to look like the whole group.

A random sample gives every member of the group the same chance to be picked.

Taking the easiest group to ask, like the first table in the lunchroom, as a random sample.

Easy to ask is not random: most students had no chance to be picked. In a random sample every member has the same chance.

Is "Number every seat in the hall, put all the numbers in a hat and draw 20 of them." a random sample? — Yes. Every member of the group has the same chance to be picked.

Estimating pizza preference from a sample of 50 of 500 students

Our school has five hundred students. How many of them like pizza for lunch?

We can't ask all five hundred! Instead, let's pick fifty students at random and ask just them. That smaller group is called a sample.

Here's our sample — fifty students chosen at random from the whole school.

After asking, thirty of the fifty say they love pizza.

Let's write that as a ratio: thirty out of fifty.

Thirty over fifty simplifies to three over five — that's sixty percent of our sample.

Here's the big idea. If sixty percent of our sample likes pizza, we estimate that about sixty percent of the whole school does too.

Sixty percent of five hundred is three hundred students. That's our estimate!

But there's a catch. For our estimate to be trustworthy, the sample MUST be random — every student needs an equal chance of being picked.

If we only asked the soccer team, almost everyone might say pizza, and we'd guess way too high. That's called a biased sample.

One more rule. The bigger our random sample, the more reliable our estimate gets.

500 students at our schoolHow many like pizza?Asking everyone would take forever…Pizza poll · 500 students totalRandom sample of 50Each block = 5 studentsSample results30 of 50 chose PIZZA3050=35=60%Estimate the whole school →60% × 500 = ?60% × 500 = 300About 300 students like pizzaOne important rule!RANDOMEvery student needs an equal chance of being picked.Otherwise our estimate can't be trusted.Biased sample — soccer team only9 of 10 said pizza → 90%?Soccer players aren't the whole school!An unfair sample → an unfair estimate.Bigger sample = better estimateSample of 10rough estimateSample of 100more reliableMore students asked → estimate closer to the truth.From sample to population60% of 500 ≈ 300 studentsA random sample reveals the whole population.ESTIMATE≈ 300of 500 students
Grade 7 · How a random sample tells us about a whole population

About three hundred of the five hundred students like pizza. A random sample lets us learn about a whole population from just a small piece. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free