Statistics · Ordinary Level
Frequency Tables
Ordinary Level · Class 4 · Tap NEXT to begin
Section 1 of 2
Reading a Frequency Table
A frequency table squashes data into two rows: the value on top, the frequency (how often) on the bottom. Goals scored in a set of games:
| Goals | 0 | 1 | 2 | 3 | 4 | 5 |
| Games | 5 | 3 | 7 | 4 | 2 | 1 |
Two quick reads
How many games (the total)? Add the bottom row. The mode? The value with the highest frequency.
Worked example — total, type, mode
For the table above: how many games, what type of data, and the mode?
Games $= 5+3+7+4+2+1 = 22$
Numerical, discrete
Mode $= 2$ goals (frequency $7$, the highest)
$22$; numerical discrete; mode $2$
You try
Using that table, how many games ended in a draw? (A draw needs an even number of goals: $0, 2$ or $4$.)
Add the frequencies for $0$, $2$ and $4$ goals.
$5 + 7 + 2 = 14$
$14$ games
Section 2 of 2
The Mean from a Frequency Table
Multiply across
Total $= \sum(\text{value} \times \text{frequency})$. Then mean $= \dfrac{\text{total}}{\text{sum of frequencies}}$.
Worked example — mean number of goals
For the goals table above, find the total goals and the mean per game.
Total $= (0\times5)+(1\times3)+(2\times7)+(3\times4)+(4\times2)+(5\times1) = 63$
Mean $= \tfrac{63}{22} \approx 2.9$
total $63$, mean $\tfrac{63}{22}$
Another set of games:
| Goals | 0 | 1 | 2 | 3 | 4 |
| Games | 7 | 3 | 5 | 2 | 1 |
You try
For this table, find (i) how many games, (ii) the total goals, (iii) how many games ended in a draw.
Games = add the bottom; goals = Σ(value×frequency); draws = frequencies for $0,2,4$.
(i) $7+3+5+2+1 = 18$ games
(ii) $(0\times7)+(1\times3)+(2\times5)+(3\times2)+(4\times1) = 23$ goals
(iii) $7+5+1 = 13$ draws
$18$ games; $23$ goals; $13$ draws
That’s Class 4.
Reading a frequency table — total, mode, and the mean via $\sum(\text{value}\times\text{frequency})$. Class 5: charts.