Data & Probability · Apply · 4.1

Which average?

Different situations call for different measures. The mean uses every value but is pulled by outliers; the median resists outliers and shows the typical middle; the mode names the most common choice. Pick the one that answers the question.

01 / THE IDEA

See it work.

Watch the method

Which average?

Outliers → median; most common → mode; balanced → mean.

1 / 2
Find the best-measure of: .
1

Add the values

Find the total of every value in the set.

NaN=NaNNaN = NaN
2

Divide by how many

The mean is the total divided by the number of values.

NaN1=NaN\frac{NaN}{1} = NaN
— / WHY IT WORKS

The idea underneath.

Right tool, right job

Choose mean, median, or mode based on outliers and what you want to know.

Why it works

An outlier? Lean on the median.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Most popular ice-cream flavor sold. Which measure?

1

Answer

Mode

EX 2medium

You want to know how spread out the data is. Which measure?

1

Answer

Range

EX 3hard

Most popular ice-cream flavor sold. Which measure?

1

Answer

Mode

04 / COMMON TRAPS

Where students slip.

Trap

Always using the mean.

Fix

Outliers distort the mean — the median may be better.

Trap

Using the mode for spread.

Fix

Spread is the range, not the mode.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

You want to know how spread out the data is. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
C2

A shoe store wants the most common size to stock. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
C3

Scores are evenly spread with no outliers. Which average fits best?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
C4

A shoe store wants the most common size to stock. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
Apply

Apply (4)

A1

Most popular ice-cream flavor sold. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
A2

Most popular ice-cream flavor sold. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
A3

A shoe store wants the most common size to stock. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
A4

Scores are evenly spread with no outliers. Which average fits best?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
Extension

Extension (4)

E1

One value is a huge outlier. Which average best shows the typical value?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
E2

A shoe store wants the most common size to stock. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
E3

A shoe store wants the most common size to stock. Which measure?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.
E4

Scores are evenly spread with no outliers. Which average fits best?

Need a hint?
  • Check for outliers.
  • Decide what the question really asks.