Question

If a population of college student ages is skewed right, then this indicates?

Answer 1

Sol:

That means mean is greater than median.

common statistical techniques are not valid for strongly skewed distributions and valid only for normal distributions.

for making the distribution normal take the logarithm of the variable age and check whether it follows normal distribution.

Positively Skewed Distribution

A positively skewed distribution is one in which the tail of the distribution shifts towards the right, i.e., it has a tail on the positive direction of the curve. For this reason, it is also called a right skewed distribution. More accurately, a distribution is said to be right skewed if its right tail is longer than its left tail. In this distribution, the mean value is towards the right side of the peak. The reason for this skewness is that the mass of the distribution occurs on the left side of the positively skewed distribution curve. This means that most values of the distribution occur on the left side

In a positively skewed distribution, the extreme scores occur on the right side and have a higher magnitude. As a rule, the mean value shifts towards the extreme scores. Since the extreme scores are larger in a right skewed distribution, the mean has a higher value. In fact, in a positively skewed distribution, both the mean and median are greater in value than the mode, and the mean will also be greater than the median value. One way of deciding whether a distribution is positively skewed or negatively skewed, is by the following formula:

Pearson's Coefficient of Skewness = (Mean - Mode) ÷ Standard deviation

The standard deviation gives the deviation of each value of the distribution from the mean. By this formula, it is clear that the value of Pearson's Coefficient will be positive for a right skewed distribution, since the mean of such a distribution is greater than its mode. This is one more reason why a right skewed distribution is called a positively skewed distribution.