A list of numbers tells you nothing. The same numbers in a table tell you everything.
Find the class width
Scores run from 12 to 87 and are to be grouped into 6 classes. What class width should be used?
The range is 87 − 12 = 75, and 75 ÷ 6 = 12.5. Class width is always rounded up, to 13 — with a width of 12 the six classes span only 72, which is not enough to hold every score. B is the rounded-down answer and leaves the top values homeless. Rounding up may leave a little room to spare, and that is fine.
| Pets owned | Tally | Frequency |
|---|---|---|
| 0 | |||| ||| | 8 |
| 1 | |||| |||| || | 12 |
| 2 | |||| |||| | 10 |
| 3 | |||| | 5 |
| total | 35 |
The frequencies must add back to the number of people surveyed. If they do not, something was counted twice or missed — check before drawing anything.
class width = range ÷ number of classes, rounded up
range = 87 − 12 = 75
highest minus lowest
75 ÷ 6 = 12.5
six classes wanted
width = 13
always round up
12–24, 25–37, 38–50, 51–63, 64–76, 77–89
six classes, no gaps, no overlaps
Writing 12–24 and 24–36 leaves a score of 24 belonging to two classes at once. The next class starts at 25. Every value must have exactly one home.
Reading the width off a finished table: subtract one class's lower limit from the next one's. Here 25 − 12 = 13, not 24 − 12 = 12, because 12–24 holds thirteen whole numbers.
12 of 35 own one pet
from the table
12 ÷ 35 ≈ 0.343
divide by the total
≈ 34.3%
× 100
0.343 × 360 ≈ 123°
its slice on a pie chart
All the relative frequencies should sum to 1, and all the pie angles to 360°. Rounding can leave you a degree short, which is normal.
| Display | Use it when |
|---|---|
| Bar graph | comparing separate categories — favourite subject, grade level |
| Histogram | showing the spread of continuous data — heights, scores |
| Pie chart | parts of one whole — how a budget divides |
| Line graph | change over time — monthly sales |
angle ÷ 360 = the share of the whole. Cumulative frequency = a running total.
In a pie chart of how 150 learners get to school, the "jeepney" sector measures 72°. What percent ride a jeepney, and how many learners is that?
72 ÷ 360 = 0.2
the sector's share of the circle
0.2 = 20%
the share as a percent
20% of 150 = 30 learners
the same share of the total count
Check forwards: 30 ÷ 150 × 360 = 72° ✓
Using the pets table in step 1, how many learners own at most 2 pets?
8, 8 + 12 = 20, 20 + 10 = 30, 30 + 5 = 35
cumulative frequencies for 0, 1, 2, 3 pets
at most 2 pets = 30
read the running total at 2
Answering 10 gives only the learners with exactly 2 pets. "At most 2" includes 0, 1 and 2 pets, which is the cumulative 30. The last cumulative frequency must equal the total, 35, or a row was missed.
The same three tools — width, share, angle — at their awkward edges.
Data runs from 30 to 91 and is grouped into 5 classes. What width should be used?
91 − 30 = 61, and 61 ÷ 5 = 12.2
not a whole number
width = 13
round up, even from 12.2
With width 12, five classes cover only 30–89 and leave 90 and 91 with no home. Rounding to the nearest is not enough; always round up.
Three tricycle routes carry 6, 9 and 15 passengers in an hour. What is the relative frequency of the second route?
total = 6 + 9 + 15 = 30
the total is not given, so add first
9 ÷ 30 = 0.3 = 30%
part over whole
Dividing by the biggest frequency (9 ÷ 15) compares two routes, not one route with the whole.
35% of a barangay's budget goes to health. What angle does that take on a pie chart?
0.35 × 360
a percent of the full circle
= 126°
a little more than a third of the circle
When the share is already a percent, there is no count to divide; go straight to × 360.
A pie chart can answer the third question at a glance but not the second — it shows proportions, never counts. If a question asks "how many", the chart must state the total somewhere.
Expect a class width, a relative frequency, a pie-chart angle (forwards or backwards), a cumulative total, or a choice of the right graph. The fastest route is "part ÷ whole", then × 100 for a percent or × 360 for an angle; the 10-second check is that the shares come to 100% and the angles to 360°.
Find the angle
In a survey of 240 learners, 54 chose basketball. What angle would basketball take on a pie chart?
Basketball's share is 54 ÷ 240 = 0.225, and 0.225 × 360 = 81°. A is the percentage (22.5%), not the angle — those are different numbers and the question asked for degrees. C copies the frequency straight into the answer, which would only be right by coincidence.
Hint: find the share as a decimal first, then multiply by 360. A percentage and a pie-chart angle are never the same number.
