Sampling variability – effect of spread of population
Heights of intermediate students
Heights of Middle School Students
Dot Plot
Intermediate
Dot Plot
Middle School
Middle School
Intermediate
height
S1 = median
S2 = Q3 height
height
153
12
S1 = median
S2 = Q3 height
Q1 height
120
140
160
180
200
height
100
120
140
160
180
200
height
Box Plot
Sample of Intermediate
120
100
120
Box Plot
Sample of Middle School
140
160
180
140
160
200
height
200
Box Plot
Sample of Middle School
Box Plot
Sample of Intermediate
120
120
180
height
140
160
180
140
160
180
200
height
200
height
Box Plot
Sample of Middle School
Box Plot
Sample of Intermediate
120
120
140
160
180
140
160
180
200
height
200
height
Box Plot
Sample of Middle School
Box Plot
Sample of Intermediate
100
120
140
160
180
120
140
200
160
180
200
height
height
120
140
160
180
Box Plot
Sample of Middle School
Box Plot
Sample of Intermediate
200
height
Lindsay Smith, University of Auckland, 2011
100
120
140
160
height
180
200
159
15
Q1 height
Sampling variability – effect of spread of population
Measures from Sample of Intermediate
100
120
140
160
An intermediate school wants to purchase new
furniture for their students, based on the median
height of students in years 7 and 8. A teacher takes a
sample of 30 intermediate students from Census at
School to make an estimate of the population
median.
Dot Plot
180
200
Median
Measures from Sample of Middle School
A middle school wants to purchase new furniture for
their students, based on the median height of middle
school students in years 7 to 10. A teacher takes a
sample of 30 middle school students from Census at
School.
Dot Plot
Which sample median is likely to give a better
estimate of the population median?
100
120
140
160
180
200
The box plots show the results of taking several
samples of size 30 from each of the populations. Also
shown is a collection of 200 medians from samples.
What do you notice?
median
Observations
Summary
Lindsay Smith, University of Auckland, 2011