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 the population IQR n

1

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

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?

weight1.5 2.0 2.5 3.0 3.5 4.0

Kiw ipop Dot Plot

3 different samples n = 303 different medians3 different IQRs

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 2Deciding 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 median2. 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. 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

EG 4) 0.1222EG 5) 1.0399EG 6) 1.0005EG 7) 1.3007EG 8) 2.2880EG 9) 1.3370EG 10)

1.4119

0.113

0.113/0.12689= 0.89

0.159

0.159/0.1075= 1.479

0.212

0.212/0.1479= 1.433

3. Divide by sample IQR/n

This gives the number of sample IQR/n that the sample median is away from the population median

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

0.113

0.113/0.12689= 0.89

0.159

0.159/0.1075= 1.479

0.212

0.212/0.1479= 1.433

3. Divide by sample IQR/n

This gives the number of sample IQR/n that the sample median is away from the population median

The final formula for the informal confidence interval is :

Final formula for informal Confidence interval