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Statistics, STD2 S1 2016 HSC 27b

A small population consists of three students of heights 153 cm, 168 cm and 174 cm. Samples of varying sizes can be taken from this population.

What is the mean of the mean heights of all the possible samples? Justify your answer.  (2 marks)

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`165\ text(cm)`

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`text(If sample is 1 person,)`

♦ Mean mark 40%.

`text{Possible mean(s): 153, 168 or 174.}`
 

`text(If sample is 2 people,)`

`text{Possible mean(s):}quad(153 + 168)/2` `= 160.5`
`(153 + 174)/2` `= 163.5`
`(168 + 174)/2` `= 171`

 

`text(If sample is 3 people,)`

`text(Mean:)quad(153 + 168 + 174)/3 = 165`
 

`:.\ text(Mean of all mean heights)`

`= (153 + 168 + 174 + 160.5 + 163.5 + 171 + 165)/7`

`= 165\ text(cm)`