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3. True or False. Justify for full credit. (a) If the variance from a data set...

3. True or False. Justify for full credit.

(a) If the variance from a data set is zero, then all the observations in this data set must be identical.

(b) The median of a normal distribution curve is always zero.

Math   Statistics-And-Probability   
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Answer #1

a) The variance of a data set is computed as:

Therefore the variance is equal to 0 for all Xi =

Therefore all observations needs to be equal for the variance to be 0. Therefore the given statement is True.

b) The median of a normal distribution is equal to its middle most point and it could be any number on the continuous number line. The median for only standard normal distribution is 0 and not for all normal distributions. Therefore the given statement is False.

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