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

1. ## 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...??

2. ## 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.

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

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

for median: 100

minimum:69.098

is this right??
Correct, well done.

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

can you help me with other question please

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

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.

6. ## 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??

7. ## 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 \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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