SME
Grade 7 Math · Statistics & Probability
Random sampling and population inferences
Use this for “In a random sample of 20 students, 6 walk to school. About how many of the 200 students walk?”
Diagram
Population N = 200, sample n = 20 picked at random.
In the sample k = 6 walk: 6/20 = 30%
E = k ÷ n × N = 6 ÷ 20 × 200 = 60
The real count, which a survey can’t see: T = 64 walk.
This is an example. Type your own values to start a new problem.
E
=
k
n
×
N
T
Whole school who walk
example
Formulas
E
=
k
÷
n
×
N
(estimate
for
the
school
=
sample
who
walk
to
school
÷
students
in
the
sample
×
students
in
the
school)
60 = 6 ÷ 20 × 200
Assumptions
•
Every student is as likely as any other to be picked: a random sample.
•
The sample’s share is about the population’s share, not exactly.
•
A bigger sample usually lands closer.
•
Take a new sample: the estimate moves a little each time.
Step-by-step
WE KNOW
N = 200 (students in the school), n = 20 (students in the sample), k = 6 (sample who walk to school), T = 64 (whole school who walk)
FIND
estimate for the school (E)
Step 1 · Find estimate for the school (E)
Use E = k ÷ n × N (estimate for the school = sample who walk to school ÷ students in the sample × students in the school)
The share who walk in the sample, times everyone in the school.
E
=
6
20
×
200
E
=
0.3
×
200
E
=
60
Check
Put the numbers back in. Both sides should match.
60 = 6 ÷ 20 × 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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