SME
Grade 9 Math · Algebra 1
Two-way frequency tables and relative frequency
Use this for “What fraction of all the students are in Grade 9 and play an instrument?” from a two-way table.
Table
80 in all: Grade 9 40, Grade 10 40
Joint relative frequency: P(Grade 9 and Plays an instrument) = 18/80 ≈ 0.23
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
n
Grand total
worked out (not typed)
p
Joint relative frequency
worked out (not typed)
Formulas
n
=
a
+
b
+
c
+
d
80 = 18 + 22 + 12 + 28
p
=
a
n
0.225
=
18
80
Assumptions
•
A relative frequency is a count divided by a total.
•
A joint relative frequency divides one cell by the grand total.
•
The row and column totals are the margins of the table.
Step-by-step
WE KNOW
a = 18, b = 22, c = 12, d = 28
FIND
grand total (n), joint relative frequency (p)
Step 1 · 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 2 · Find joint relative frequency (p)
Use p = a ÷ n
One cell out of everyone: Grade 9 and plays.
p
=
18
80
p
=
0.225
Check
Put the numbers back in. Both sides should match.
80 = 18 + 22 + 12 + 28 ✓
0.225
=
18
80
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.