# help with finding five-number summary when mean, sd and sample size is given

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• Aug 23rd 2012, 09:21 PM
ch5112
Re: help with finding five-number summary when mean, sd and sample size is given
value i found for maximum is: 130.90

for median: 100

minimum:69.098

correct...? or...??
• Aug 23rd 2012, 09:22 PM
ch5112
Re: help with finding five-number summary when mean, sd and sample size is given
I have another question...

According to the IQR rule, an observation is labelled as a potential outlier if it is more than
1.5xIQR above the upper quartile, or 1.5xIQR below the lower quartile, where IQR denotes the
inter-quartile range. Show that, for a sample from a normally distributed population the IQR rule
identifies any observation that is more than 2.7 standard deviations from the mean as an outlier.
• Aug 23rd 2012, 09:32 PM
Prove It
Re: help with finding five-number summary when mean, sd and sample size is given
Quote:

Originally Posted by ch5112
value i found for maximum is: 130.90

for median: 100

minimum:69.098

is this right??

Correct, well done.
• Aug 23rd 2012, 09:36 PM
ch5112
Re: help with finding five-number summary when mean, sd and sample size is given
can you help me with other question please
• Aug 23rd 2012, 09:38 PM
Prove It
Re: help with finding five-number summary when mean, sd and sample size is given
Quote:

Originally Posted by ch5112
I have another question...

According to the IQR rule, an observation is labelled as a potential outlier if it is more than
1.5xIQR above the upper quartile, or 1.5xIQR below the lower quartile, where IQR denotes the
inter-quartile range. Show that, for a sample from a normally distributed population the IQR rule
identifies any observation that is more than 2.7 standard deviations from the mean as an outlier.

Well, you know that in the standard normal distribution, the lower quartile is -0.6745 and the upper quartile is 0.6745. So the interquartile range is the distance between these values, IQR = 1.349 and 1.5 x IQR = 1.5 x 1.349 = 2.0235.

So add this value to the upper quartile and you get about 2.7, similarly, subtracting this value from the lower quartile gives you about -2.7. So any values more than 2.7 standard deviations from the mean are considered to be outliers.
• Aug 23rd 2012, 09:42 PM
ch5112
Re: help with finding five-number summary when mean, sd and sample size is given
i see... is there any more reasoning that i can add??
• Aug 23rd 2012, 09:44 PM
Prove It
Re: help with finding five-number summary when mean, sd and sample size is given
What more reasoning would you need? Your interval for acceptable values in a data set are \displaystyle \displaystyle \begin{align*} \left[ Q_L - 1.5 \, IQR , Q_U + 1.5 \, IQR \right] \end{align*}, I've just taught you how to get this...
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