Revision notes
Organise raw data into a frequency table, then read off the mode, median and mean without writing every number out.
Mr Eze sells school shoes in Aba. Writing down the size of every one of 200 customers gives a messy list. A frequency table shrinks it to a few neat rows — and shows him that size 39 sells the most.
Raw data is the list exactly as it was collected, e.g. goals in 12 matches: 1, 0, 2, 1, 3, 1, 0, 2, 1, 4, 2, 1.
In a frequency table each value is written once, with a tally and its frequency (how many times it appears). Here: 0 → 2, 1 → 5, 2 → 3, 3 → 1, 4 → 1.
Check: the frequencies add up to the number of values, 2 + 5 + 3 + 1 + 1 = 12.
🔑 Key idea: Σf (the sum of the frequencies) = the number of values.
The mode is the value with the highest frequency — here 1 goal (frequency 5). Don't give the frequency 5 as the answer!
For the median, find its position first: with n values it is the (n + 1) ÷ 2 th value. Then keep a running total of the frequencies until you pass that position.
With 12 values, the median is halfway between the 6th and 7th. Running totals: 0 → 2, 1 → 7. So the 6th and 7th are both 1, and the median is 1.
🔑 Key idea: Mode = value with the highest frequency. Median: find the position, then use running totals.
Each value appears f times, so multiply: fx = value × frequency. Adding these gives the total of all the data, Σfx.
Goals: 0×2 + 1×5 + 2×3 + 3×1 + 4×1 = 0 + 5 + 6 + 3 + 4 = 18 goals in 12 matches.
Mean = Σfx ÷ Σf = 18 ÷ 12 = 1.5 goals per match.
🔑 Key idea: Mean = Σfx ÷ Σf.
The marks scored by some students in a quiz are shown as mark (frequency): 10 (7), 20 (4), 30 (8), 40 (8), 50 (5). Find the mean mark.
Step 1: Multiply each mark by its frequency
10 × 7 = 70, 20 × 4 = 80, 30 × 8 = 240, 40 × 8 = 320, 50 × 5 = 250
Step 2: Add
Σfx = 960
Σf = 32
Step 3: Divide
Mean = 960 ÷ 32 = 30
Answer: 30
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