Answer to Question #323614 in Statistics and Probability for Toilet Gamer

Question

The average on a history exam was 85 out of 100 points, with a standard deviation of 15. Was the distribution of the scores on this exam symmetric? If not, what shape would you expect this distribution to have? Explain your reasoning.

Answer 1

The distribution is not symmetrical. It is skewed to the right.

In a symmetric distribution, the mean and the median are equal. Also, the distribution can be equally divided into half, with each half having similar property.

From the data given, the mean of the distribution, M= 85

The median of the distribution will be 50.5

The mean and the median are not equal, the shape cannot be symmetrical

In addition, the standard deviation, d = 15

1 standard deviation above the mean = d + M= 15 + 85 = 100

This shows that there is only 1 standard deviation above mean and more than 3 standard deviation below the mean, hence the shape cannot be symmetrical.