SME
Grade 8 Math · Problem type
Two-way tables
Use this for “Of 40 students with a pet, 30 have a sibling; of 60 without a pet, 30 do. Is there an association?”
Chart
g = 25% (gap between the percents)
This is an example. Type your own values to start a new problem.
a
Pet and sibling
example
b
Pet, no sibling
example
c
No pet, sibling
example
d
No pet, no sibling
example
R₁
With a pet
worked out (not typed)
R₂
Without a pet
worked out (not typed)
p₁
With a pet: share with a sibling
worked out (not typed) · %
p₂
Without: share with a sibling
worked out (not typed) · %
g
Gap between the percents
worked out (not typed) · %
Formulas
R₁
=
a
+
b
(with
a
pet
=
pet
and
sibling
+
pet,
no
sibling)
40 = 30 + 10
R₂
=
c
+
d
(without
a
pet
=
no
pet,
sibling
+
no
pet,
no
sibling)
60 = 30 + 30
p₁
=
a
÷
R₁
×
100
(with
a
pet:
share
with
a
sibling
=
pet
and
sibling
÷
with
a
pet
×
100)
75 = 30 ÷ 40 × 100
p₂
=
c
÷
R₂
×
100
(without:
share
with
a
sibling
=
no
pet,
sibling
÷
without
a
pet
×
100)
50 = 30 ÷ 60 × 100
g
=
p₁
−
p₂
(gap
between
the
percents
=
with
a
pet:
share
with
a
sibling
−
without:
share
with
a
sibling)
25 = 75 − 50
Assumptions
•
Each cell counts people in both groups at once: a pet and a sibling, a pet and no sibling, …
•
Compare the rows as percents, not counts, when the rows differ in size.
•
Very different percents suggest an association; about the same, none.
Step-by-step
WE KNOW
a = 30 (pet and sibling), b = 10 (pet, no sibling), c = 30 (no pet, sibling), d = 30 (no pet, no sibling)
FIND
with a pet (R₁), without a pet (R₂), with a pet: share with a sibling (p₁), without: share with a sibling (p₂), gap between the percents (g)
Step 1 · Find with a pet (R₁)
Use R₁ = a + b (with a pet = pet and sibling + pet, no sibling)
Everyone with a pet: the first row’s total.
R₁
=
30
+
10
R₁
=
40
Step 2 · Find without a pet (R₂)
Use R₂ = c + d (without a pet = no pet, sibling + no pet, no sibling)
Everyone without a pet: the second row’s total.
R₂
=
30
+
30
R₂
=
60
Step 3 · Find with a pet: share with a sibling (p₁)
Use p₁ = a ÷ R₁ × 100 (with a pet: share with a sibling = pet and sibling ÷ with a pet × 100)
The share of the first row with a sibling, as a percent.
p₁
=
30
40
×
100
p₁
=
0.75
×
100
p₁
=
75%
Step 4 · Find without: share with a sibling (p₂)
Use p₂ = c ÷ R₂ × 100 (without: share with a sibling = no pet, sibling ÷ without a pet × 100)
The share of the second row with a sibling.
p₂
=
30
60
×
100
p₂
=
0.5
×
100
p₂
=
50%
Step 5 · Find gap between the percents (g)
Use g = p₁ − p₂ (gap between the percents = with a pet: share with a sibling − without: share with a sibling)
The percents differ a lot: that suggests an association.
g
=
75
−
50
g
=
25%
Check
Put the numbers back in. Both sides should match.
40 = 30 + 10 ✓
60 = 30 + 30 ✓
75 = 30 ÷ 40 × 100 ✓
50 = 30 ÷ 60 × 100 ✓
25 = 75 − 50 ✓
Topic check
See what you know: 5 questions on this topic
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