SME
Grade 9 Math · Problem type
Marginal relative frequency
Use this for “What fraction of all the students play an instrument?”
Table
80 in all: Grade 9 40, Grade 10 40
Marginal relative frequency: P(Plays an instrument) = 30/80 ≈ 0.38
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
C
Plays an instrument, total
worked out (not typed)
n
Grand total
worked out (not typed)
p
Marginal relative frequency
worked out (not typed)
Formulas
C
=
a
+
c
30 = 18 + 12
n
=
a
+
b
+
c
+
d
80 = 18 + 22 + 12 + 28
p
=
C
n
0.375
=
30
80
Assumptions
•
A marginal relative frequency uses a total at the edge of the table.
•
Divide a column (or row) total by the grand total.
Step-by-step
WE KNOW
a = 18, b = 22, c = 12, d = 28
FIND
plays an instrument, total (C), grand total (n), marginal relative frequency (p)
Step 1 · Find plays an instrument, total (C)
Use C = a + c
The column total: everyone who plays.
C
=
18
+
12
C
=
30
Step 2 · Find grand total (n)
Use n = a + b + c + d
The grand total: add all four cells.
n
=
18
+
22
+
12
+
28
n
=
80
Step 3 · Find marginal relative frequency (p)
Use p = C ÷ n
The column total out of everyone.
p
=
30
80
p
=
0.375
→
30
80
=
3
8
=
0.375
Check
Put the numbers back in. Both sides should match.
30 = 18 + 12 ✓
80 = 18 + 22 + 12 + 28 ✓
0.375
=
30
80
✓
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Two-way frequency tables and relative frequency
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Conditional relative frequency
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