3. Suppose we have a sample of four valuesX1,X2,X3,X4, where all of theXiare val

Question

3. Suppose we have a sample of four valuesX1,X2,X3,X4, where all of theXiare values inthe set{1,2,3,4,5,6,7,8,9,10}.

(a) What 4 different numbers (i.e., no repeats allowed) from the set {1,2,3,4,5,6,7,8,9,10} will give the largest possible standard deviation?

(b) If repeats are allowed, what 4 numbers from the set {1,2,3,4,5,6,7,8,9,10} will give the largest possible standard deviation?

Hint: You do not need to calculate any standard deviations to answer this question. If you understand what standard deviation is measuring, the answers should be very easy. Try to answer these questions without doing any calculations.

Explanation / Answer

Standard deviation is the measure of dispersion. it measures variability in the data set that is deviation of each data point from the mean.

If the data points are away from the mean then the variabiltiy would be more it results into large value of standard deviation.

If data points are closer then variability is less, it results into smaller value of standard deviation.

So according to this for part a) sample {1,2,9,10} has the largest standard deviation value.

Part b) if repeatations allowed the sample {1,1,10,10} has the largest standard deviation value.

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