Kiwi kapers 3
Relationship between the width of the IQR for
sample medians of sample size n and the
population IR and the sample size…
 IQR for sample medians (sample size = n) is
approximately of 1 the population IQR
n
Developing an informal
confidence interval for the
population median…
 For our informal confidence interval for the
population median we want to use
 Sample median
 Sample IQR/n
 We need to see how big to make this interval
so we’re pretty sure the interval includes the
population median
 We want it to work about 90% of the time
 Remember we’re in TEACHING WORLD
 We’re going to explore how wide our intervals
should be when we can work backwards from
a given population.
 Informal confidence intervals…
sample median  k x sample IQR/n
Dot Plot
Kiw ipop
3 different samples n = 30
3 different medians
3 different IQRs
1.5
2.0
2.5
3.0
3.5
w eight
Movable line is at 2.53
 What would be the ideal number (k) of
sample IQR/ n to use all the time to be
pretty sure the interval includes the
population median?
4.0
That is…
 We know what the population median
actually is
 We can look and see how far away from the
population median this is:
sample IQR/sqrt(n)
Worksheet 2
Deciding how many sample IQR/n we need
for the informal confidence interval
(finding k)
For each example…
1. Mark the sample median on the big graph and draw
a line to the population median
2. Find the distance the sample median is from the
population median (2.529kg)
3. Divide by sample IQR/n
 This gives the number of sample IQR /n that the
sample median is away from the population median
 THIS IS THE NUMBER WE ARE INTERESTED IN
1.
2.
3.
Mark the sample
median on the big
graph and draw a
line to the
population
median
Find the distance
the sample
median is from
the population
median (2.529kg)
Divide by sample
IQR/n
0.113
3. Divide by sample IQR/n
0.113/0.12689
= 0.89
This gives the number of
sample IQR/n that the
sample median is away from
the population median
0.159
0.159/0.1075
= 1.479
0.212
0.212/0.1479
= 1.433
EG 4) 0.1222
EG 5) 1.0399
EG 6) 1.0005
EG 7) 1.3007
EG 8) 2.2880
EG 9) 1.3370
EG 10) 1.4119
0.113
3. Divide by sample IQR/n
0.113/0.12689
= 0.89
This gives the number of
sample IQR/n that the
sample median is away from
the population median
0.159
0.159/0.1075
= 1.479
0.212
0.212/0.1479
= 1.433
From our 10
samples it
would appear
±1.5 x
IQR/sqrt(n)
would be
most
effective.
That is… it
should
capture the
population
median most
of the time
Final formula for informal
Confidence interval
The final formula for the informal confidence interval is :