You give up knowing which mark belonged to whom, and in exchange you can see the shape of the whole set.
Tally marks and frequency
Group the tallies in fives, because a human eye counts fives far more reliably than eleven separate strokes.
Read the list once, in order. Always check at the end that the frequencies add up to the number of pieces of data you started with.
Grouping into classes
Six to ten classes usually works well: too few and the detail disappears, too many and the shape does not appear.
0 to 10 then 10 to 20 leaves a mark of 10 in two classes. 0 to 9 then 11 to 20 leaves it in none. Every value must fit exactly one class.
| Term | What it means | For the class 20 to 29 |
|---|---|---|
| Class limits | The smallest and largest values it holds | 20 and 29 |
| Class size | How many values it covers | 10 |
| Class mark | The middle value | 24.5 |
| Frequency | How many pieces of data fall in it | Whatever the tally gives |
Once you know seven students scored between 20 and 29, you no longer know whether they scored 20 or 29. Keep the original list.
Frequencies 3, 5, 7 and 4 give cumulative figures 3, 8, 15 and 19. The last one must equal the total number of pieces of data.
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