If the sum of squared deviations of gas prices is zero what

If the sum of squared deviations of gas prices is zero, what can you infer about:

a) its variance

b) its mean, median and mode

c) its usefulness in statistics

In general, if the mode is to the left of the median and the mean is to its right, what can you infer about the skewness of the distribution? (There are exceptions!)

Solution

a)

Note that

variance = SS/(n-1)

As SS = 0, then

variance = 0 [ANSWER]

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b)

As SS = 0, then allthe entries must all be the same/equal.

Hence, the mean, median, and mode are all equal as well.

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c)

If SS = 0, we can already tell that all the entries are equal.

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d)

It is usually a positively skewed distirbution when mean > median, and mode > median. [ANSWER, POSITIVELY SKEWED]