Foundation and Higher · mean from a table
Mean from a
frequency table.
Add a column.
divide by the total
frequency, not the rows
a table is a shorter way to write a list —
Frequency
“goals 2, frequency 5” means
2, 2, 2, 2, 2: five lots of two
step 1 of 4
Add an fx column
1. Multiply each value by its frequency.
2. Total both columns: 20 games, 31 goals.
✓ 31 goals in 20 games
| goals | frequency | goals × freq |
|---|
| 0 | 4 | 0 |
| 1 | 6 | 6 |
| 2 | 5 | 10 |
| 3 | 5 | 15 |
| total | 20 | 31 |
step 2 of 4
Divide the totals
1. Total of the new column on top.
2. Total frequency underneath: 20, not 4.
✓ Not by the number of rows
mean = total goalstotal games
= 3120
= 1.55 goals per game
step 3 of 4
Grouped: midpoints
1. You do not know the exact values.
2. So use the middle of each group.
✓ 140 ÷ 10 = 14: an estimate of the mean
| time | freq | midpoint | mid × freq |
|---|
| 0 < t ≤ 10 | 3 | 5 | 15 |
| 10 < t ≤ 20 | 5 | 15 | 75 |
| 20 < t ≤ 30 | 2 | 25 | 50 |
| total | 10 | | 140 |
step 4 of 4
Modal class, median
1. Modal class: the group with most in it.
2. Median: count through the frequencies.
✓ Give the class, not the frequency
modal class: 10 < t ≤ 20
median: 10 values, so the 5th and 6th
3 + 5 = 8: the middle group
mean from a table —
New column
value × frequency
Divide
its total ÷ total frequency
Grouped
use midpoints: an estimate
Sense check: the mean must sit
inside the range of the data.
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