# Kiwi kapers 3 - PowerPoint PPT Presentation

1 / 11

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Kiwi kapers 3

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### 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

### 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?

3 different samples n = 30

3 different medians

3 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…

• 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

• 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

• 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

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

0.113/0.12689

= 0.89

3. Divide by sample IQR/n

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

0.113

0.113/0.12689

= 0.89

3. Divide by sample IQR/n

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

### Final formula for informal Confidence interval

The final formula for the informal confidence interval is :