EXAMPLE 3.2.6

The frequency table below represents the distribution of scores on a ten-point quiz. Compute the mean, median, and mode for this distribution.

Quiz Scores

EXAMPLE 3.2.6 SOLUTION

MODE

The mode = 10, since that is the value with the highest frequency.

The mean and median both require that we find n, the population size.

n = sum of frequencies = 6 + 8 + 14 + 22 + 28 + 36 = 114

MEAN

= 8.46 (this has been rounded)

MEDIAN

To find the median, we use the fact that the position of the middle value is

Since 57.5 is between 57 and 58, the median is determined by the average of the 57th and 58th numbers on the list. We make a column for cumulative frequency, filling it in until we locate the 57th and 58th numbers:

The table above shows us that the 51st through 78th numbers are all 9s; in particular then, the 57th and 58th numbers on the list are 9s.

The median is 9.