Summarizing Data with Tables

A table should make the denominator visible

A frequency table lists values or categories and their counts. Relative frequency divides each count by a stated total. Include zero-count categories when their absence matters, and give missing responses their own accounting.

In a hypothetical survey of 20 deliveries, 8 use standard, 6 express, 4 pickup and 2 have no recorded method.

Method	Count	Share of all 20	Share of 18 recorded
Standard	8	40.0%	44.4%
Express	6	30.0%	33.3%
Pickup	4	20.0%	22.2%
Missing	2	10.0%	Not included

Both percentage columns can be useful, but they answer different questions. A label such as “44.4% of recorded responses” prevents a silent change in denominator. Rounded percentages need not add to exactly 100%.

Group numerical values without overlapping bins

Suppose durations in minutes are 2, 3, 3, 4, 6, 7, 8, 10. Choose intervals that cover each observation exactly once.

Duration	Frequency	Relative frequency	Cumulative count
0 ≤ duration < 5	4	50%	4
5 ≤ duration < 10	3	37.5%	7
10 ≤ duration < 15	1	12.5%	8

The boundaries explain why 10 belongs in the final row. Cumulative counts are meaningful here because durations have an order. Adding up shipping categories in an arbitrary order does not produce a meaningful cumulative distribution.

Grouping loses information. These bins cannot recover the exact original mean or median. Keep the raw data when possible, and choose bins for readability rather than to create a desired pattern. For unequal-width histogram bins, probability or relative frequency corresponds to area, not height alone.

Two-way tables distinguish row and column questions

Consider a hypothetical completion study:

Version	Completed	Did not complete	Assigned total
A	80	120	200
B	100	100	200
Total	180	220	400

“Which version has a higher completion rate?” uses row totals: A = 80/200 = 40%, B = 100/200 = 50%. “What fraction of completers used B?” uses the completed column: 100/180 = 55.6%. The latter is not B’s completion rate.

Unequal group sizes make raw completed counts especially misleading. Preserve counts even when reporting percentages; counts support uncertainty calculations and reveal tiny denominators. A table describes the observed data, while population inference needs a sampling or experimental model.

Practice

In the delivery table, what percentage of all deliveries used pickup? What percentage of recorded methods were pickup?

Show the explanation

The first is 4/20 = 20%. The second is 4/18 ≈ 22.2%. Neither denominator can silently stand in for the other. Report the two missing methods as well.

Continue

Turn the counts into graphs, or learn how a chi-square test uses a two-way table. OpenStax explains frequency tables and relative frequency.