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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.

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Kiwi kapers 3
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


Developing an informal confidence interval for the population median
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 population median…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… population median…

    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
That is… population median…

  • 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
Worksheet 2 population median…Deciding 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



EG 4) 0.1222 the population median

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/ the population mediansqrt(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
Final formula for informal Confidence interval the population median

The final formula for the informal confidence interval is :


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