Mean from Tables

GCSE MATHS • HIGHER TIER

Mean from Tables Made Simple

Calculate the mean from frequency tables using values, frequencies and fx totals with a clear GCSE method.

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Worked proofs

Mean from Tables in Four Moves

1

Multiply

Multiply each value x by its frequency f.

2

Total

Add the fx values and add the frequencies.

3

Divide

Divide the total fx by the total frequency.

4

Check

Make sure the answer is sensible for the values in the table.

What You’ll Learn

Understand the Mean

Know what the mean represents as an average.

Use Frequency Tables

Work efficiently with repeated values.

Calculate fx

Multiply each value by its frequency.

Apply the Mean Formula

Use total fx divided by total frequency.

Extend to Grouped Tables

Understand that grouped data usually uses class midpoints.

Key Rules

The formula for finding the mean from a frequency table is :

Mean = Σfx ÷ Σf

where :
• f = frequency
• x = value
• fx = frequency × value
• Σ means total

This formula is one of the most important formulas in GCSE Statistics.

Worked Proof: Mean from Tables

Step-by-Step Method

  • 1. Write the values and frequencies.
  • 2. Multiply each value by its frequency.
  • 3. Calculate the total of the fx column.
  • 4. Calculate the total frequency.
  • 5. Divide Σfx by Σf.
  • 6. Write the final answer.

More Worked Examples

1

Value: 2, 4, 6

Frequency: 3, 2, 5

2 × 3 = 6
4 × 2 = 8
6 × 5 = 30
Total fx = 44
Total frequency = 10
Mean = 44 ÷ 10 = 4.4
Answer: 4.4

2

Value: 1, 2, 3, 4

Frequency : 5, 4, 3, 2

Total fx = 30
Total frequency = 14
Mean = 30 ÷ 14 ≈ 2.14
Answer: 2.14

3

Value: 10, 20, 30

Frequency: 2, 3, 1

fx values : 20, 60, 30
Total fx = 110
Total frequency = 6.
Mean = 110 ÷ 6 ≈ 18.33
Answer: 18.33

4

Value: 5, 10, 15

fx values : 20, 50, 15

Total fx = 85
Total frequency = 10
Mean = 8.5
Answer: 8.5
  • Common GCSE Mistakes
  • Multiplication : Do not forget to multiply each value by its frequency.
  • Divisor : Divide by the total frequency, not the number of rows.
  • fx arithmetic : Check every multiplication in the fx column.
  • Totals : Add both the fx column and frequency column carefully.
  • Exam Tips
  • Write the formula Mean = Σfx ÷ Σf before starting.
  • Create an fx column to organise the calculation clearly.
  • Check that Σf is the total number of data values.
  • Use a calculator carefully for multiplication and division.
  • Check that the mean lies within a sensible range for the data.

Skills Used in Mean from Tables

Averages

Frequency Tables

Multiplication

Column Totals

Mean Formula

Grouped Frequency Tables

Statistics

Data Handling

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Frequently Asked Questions

An arc is a section of the circumference of a circle.

Arc Length = (Angle ÷ 360) × Circumference.

A full circle contains 360°, so this gives the required fraction of the circumference.

Yes, unless a decimal answer is specifically requested.

Use linear units such as cm, m or mm.

The arc is the curved boundary of a sector and uses the same central angle.