SME
Cartography · Problem type
Rates, not counts, on a choropleth
Use this for “County A has 340 cases among 85,000 people; county B has 900 among 450,000. Which county should be shaded darker on a choropleth?”
Chart
This is an example. Type your own values to start a new problem.
nA
Cases in A
example
PA
Population of A
example
rA
Rate in A, per 100,000
calculated
nB
Cases in B
example
PB
Population of B
example
rB
Rate in B, per 100,000
calculated
RR
Rate ratio, A to B
calculated
Formulas
rA
=
100,000
×
nA
PA
400
=
100,000
×
340
85,000
rB
=
100,000
×
nB
PB
200
=
100,000
×
900
450,000
RR
=
rA
rB
2
=
400
200
Assumptions
•
A choropleth shades whole areas, so big counties look important whatever their counts: shade a rate, never a raw count.
•
A rate per 100,000 people is cases ÷ population × 100,000, so counties of any size compare.
•
Small populations give jumpy rates: a few cases more or less swing them widely.
Step-by-step
WE KNOW
nA = 340, PA = 85,000, nB = 900, PB = 450,000
FIND
rate in A, per 100,000 (rA), rate in B, per 100,000 (rB), rate ratio, A to B (RR)
Step 1 · Find rate in A, per 100,000 (rA)
Use rA = 100,000 × nA ÷ PA
Cases for each person, scaled up to cases per 100,000 people.
rA
=
100,000
×
340
85,000
rA
=
34,000,000
85,000
rA = 400
Step 2 · Find rate in B, per 100,000 (rB)
Use rB = 100,000 × nB ÷ PB
Cases for each person, scaled up to cases per 100,000 people.
rB
=
100,000
×
900
450,000
rB
=
90,000,000
450,000
rB = 200
Step 3 · Find rate ratio, A to B (RR)
Use RR = rA ÷ rB
How many times B’s rate A’s rate is: above 1, A is shaded darker.
RR
=
400
200
RR = 2
Check
Put the numbers back in. Both sides should match.
400
=
100,000
×
340
85,000
✓
200
=
100,000
×
900
450,000
✓
2
=
400
200
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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