Mean from a Frequency Table
Grade 4Why you can't just add and divide
When data is in a frequency table, you don't have a list of individual values — you have each value (or group) and how often it appears. You need to account for the frequency before dividing.
Mean = Σ(x × f) ÷ Σf
In plain English: multiply each value by its frequency, add up all those products, then divide by the total frequency.
Worked example — simple frequency table
EXAMPLE
A frequency table shows: Score 2 (frequency 3), Score 3 (frequency 5), Score 4 (frequency 2). Find the mean.
Multiply each score by its frequency: (2 × 3) + (3 × 5) + (4 × 2) = 6 + 15 + 8 = 29.
Total frequency: 3 + 5 + 2 = 10.
Mean = 29 ÷ 10 = 2.9
Grouped data — use the midpoint
When data is grouped (e.g. "10 ≤ x < 20"), you don't know the exact values. Use the midpoint of each class as your estimate for x.
EXAMPLE
Heights (cm): 140 ≤ x < 150 (freq 4), 150 ≤ x < 160 (freq 7), 160 ≤ x < 170 (freq 3). Estimate the mean.
Midpoints: 145, 155, 165.
Σ(x × f): (145 × 4) + (155 × 7) + (165 × 3) = 580 + 1085 + 495 = 2160.
Σf = 4 + 7 + 3 = 14.
Mean estimate = 2160 ÷ 14 ≈ 154.3 cm
Because you're using midpoints rather than actual values, the answer is an estimate of the mean. Exam mark schemes usually accept answers within a small rounding tolerance.
