Although the three measures of central tendency appear to be very simple to calculate, there is always a chance for errors. The most common sources of error are listed next.

a. Many students find it very difficult to compute the mean for data presented in a frequency distribution table. They tend to ignore the frequencies in the table and simply average the score values listed in the X column. You must use the frequencies and the scores! Remember that the number of scores is found by N 5 Sf, and the sum of all N scores is found by SfX. For the distribution shown in the margin, the mean is 24 10 5 2.40.

b. The median is the midpoint of the distribution of scores, not the midpoint of the scale of measurement. For a 100-point test, for example, many students incorrectly assume that the median must be X 550.

To find the median, you must have the complete set of individual scores. The median separates the individuals into two equal-sized groups.

c. The most common error with the mode is for students to report the highest frequency in a distribution rather than the score with the highest frequency. Remember that the purpose of central tendency is to find the most representative score. For the distribution in the margin, the mode is X 5 3, not f 5 4.