Mean from a Frequency Table

Grade 4

Why 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.

Try this one

Six numbers have a mean of 9 and a range of 8.

The smallest number is 5.

(a) What is the largest number? [1]

(b) What is the total of all six numbers? [1]

Nova's hint:

Range and mean are two different statistical measures you can use to find missing information.

Ask yourself: 'How is the range calculated from the largest and smallest values, and how does the mean relate to the total?'

Remember: range = largest − smallest, and total = mean × number of values.

Try to Solve it with Nova?