Data & Probability · Working with data · 2.1

Find a missing value.

If you know the target mean, you can find a missing value: the total must equal mean × count. For values 4, 6, 8 to average 7 across four numbers, the total must be 28, so the missing value is 28 − 18 = 10.

01 / THE IDEA

See it work.

Watch the method

Find a missing value

Needed total = mean × count; subtract what you have.

1 / 2
What value must be added to 4,6,8 to make the mean 7?
1

Total needed

For a mean of 7 across 4 values, the total must be 7×4.

7×4=287\times 4 = 28
2

Subtract what you have

Take away the current total to find the missing value.

28−18=1028 - 18 = 10
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type the answer — a fraction or decimal is fine.

streak 0
best 0

…

— / WHY IT WORKS

The idea underneath.

Work backwards

The mean fixes the total; the missing value is the total minus the known sum.

Why it works

Reverse the mean.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

What value must be added to 5,9,6,9 to make the mean 8?

1

Total needed

For a mean of 8 across 5 values, the total must be 8×5. 8× 5 = 40

2

Subtract what you have

Take away the current total to find the missing value. 40 - 29 = 11

EX 2medium

What value must be added to 3,7,7,7 to make the mean 6?

1

Total needed

For a mean of 6 across 5 values, the total must be 6×5. 6× 5 = 30

2

Subtract what you have

Take away the current total to find the missing value. 30 - 24 = 6

EX 3hard

What value must be added to 2,3,6,7 to make the mean 7?

1

Total needed

For a mean of 7 across 5 values, the total must be 7×5. 7× 5 = 35

2

Subtract what you have

Take away the current total to find the missing value. 35 - 18 = 17

04 / COMMON TRAPS

Where students slip.

Trap

Using the old count.

Fix

Include the missing value in the count.

Trap

Forgetting to subtract the known sum.

Fix

Required total − current sum = missing value.

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

What value must be added to 7,7,2,4 to make the mean 7?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
C2

What value must be added to 6,6,3 to make the mean 7?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
C3

What value must be added to 9,5,4 to make the mean 4?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
C4

What value must be added to 6,8,6 to make the mean 4?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
Apply

Apply (4)

A1

What value must be added to 3,8,3,4 to make the mean 6?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
A2

What value must be added to 2,4,8 to make the mean 8?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
A3

What value must be added to 5,7,7,9 to make the mean 6?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
A4

What value must be added to 3,5,7,3 to make the mean 4?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
Extension

Extension (4)

E1

What value must be added to 5,4,3 to make the mean 8?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
E2

What value must be added to 7,8,3 to make the mean 4?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
E3

What value must be added to 9,6,9,9 to make the mean 6?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.
E4

What value must be added to 4,9,8,3 to make the mean 8?

Need a hint?
  • Required total = mean × (count including the new value).
  • Subtract the values you already have.