Question

Each year about 1,200 students take the introductory statistics course at a large university. This year scores on the final exam are distributed with a median of 73 points, a mean of 71 points, and a standard deviation of 10 points. There are no students who scored above 100 (the maximum score attainable on the nal) but a few students scored below 20 points.(a) Is the distribution of scores on this nal exam symmetric, right skewed, or left skewed?

Answer 1

The distribution of the scores is left or negatively skewed.

Explanation:

A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the distribution.

A distribution is said to be skewed to the left, or negatively skewed, if maximum of the data are collected on the right of the distribution.

A distribution is said to be symmetric when the data is distributed at regular frequencies, i.e. there is as many values on the left part of the graph as on the right.

In case of a positively skewed distribution the relationship between mean and median is:

Mean > Median

In case of a negatively skewed distribution the relationship between mean and median is:

Mean < Median

And in case of a symmetrical distribution the relationship between mean and median is:

Mean = Median

It is provided that the mean and median of the scores on the final exam are:

Mean = 71

Median = 73

So, it is obvious that:

Mean < Median

Hence, the distribution of the scores is left or negatively skewed.