SME
Grade 9 Math · Problem type
Conditional relative frequency
Use this for “Of the Grade 9 students, what fraction play? Is grade linked to playing?”
Table
80 in all: Grade 9 40, Grade 10 40
Conditional relative frequency: P(Plays an instrument | Grade 9) = 18/40 = 0.45, out of the Grade 9 total only
This is an example. Type your own values to start a new problem.
a
Grade 9, plays an instrument
example
b
Grade 9, does not
example
c
Grade 10, plays an instrument
example
d
Grade 10, does not
example
R₁
Grade 9 total
worked out (not typed)
R₂
Grade 10 total
worked out (not typed)
p₁
Share of Grade 9 who play
worked out (not typed)
p₂
Share of Grade 10 who play
worked out (not typed)
g
Gap between the rows
worked out (not typed)
Formulas
R₁
=
a
+
b
40 = 18 + 22
R₂
=
c
+
d
40 = 12 + 28
p₁
=
a
R₁
0.45
=
18
40
p₂
=
c
R₂
0.3
=
12
40
g
=
p₁
−
p₂
0.15 = 0.45 − 0.3
Assumptions
•
A conditional relative frequency divides a cell by its own row total.
•
Compare the rows: if their fractions differ, the two variables are associated.
•
If every row has the same fraction, there is no association.
Step-by-step
WE KNOW
a = 18, b = 22, c = 12, d = 28
FIND
grade 9 total (R₁), grade 10 total (R₂), share of Grade 9 who play (p₁), share of Grade 10 who play (p₂), gap between the rows (g)
Step 1 · Find grade 9 total (R₁)
Use R₁ = a + b
The row total for Grade 9.
R₁
=
18
+
22
R₁
=
40
Step 2 · Find grade 10 total (R₂)
Use R₂ = c + d
The row total for Grade 10.
R₂
=
12
+
28
R₂
=
40
Step 3 · Find share of Grade 9 who play (p₁)
Use p₁ = a ÷ R₁
Of the Grade 9 students, the fraction who play.
p₁
=
18
40
p₁
=
0.45
→
45%
Step 4 · Find share of Grade 10 who play (p₂)
Use p₂ = c ÷ R₂
Of the Grade 10 students, the fraction who play.
p₂
=
12
40
p₂
=
0.3
→
30%
Step 5 · Find gap between the rows (g)
Use g = p₁ − p₂
Compare the rows: a large gap between them suggests grade and playing are associated.
g
=
0.45
−
0.3
g
=
0.15
Check
Put the numbers back in. Both sides should match.
40 = 18 + 22 ✓
40 = 12 + 28 ✓
0.45
=
18
40
✓
0.3
=
12
40
✓
0.15 = 0.45 − 0.3 ✓
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