Mean, Media, and Mode

All these three are central tendencies. They are central score among a set of scores. Mean is heavily influenced by extreme values hence is not suitable for measuring process performance.

[Mean is also called average; median is the middle value in a set of sorted data; mode is the value repeating most of the times]

An illustration representing the fallibility of Mean and merit of Median is given below:

These are the marks obtained by students in mathematics in a particular class.

Marks
95
45
34
67
78
99
87
89
67
56
45
65
65
67
87
84
96

Here, the mean is 66.65, and the median is 67. If the mathematics teacher is asked to improve the MEAN MARKS BY 20 (i.e. performance should be so enhanced that mean becomes 80), it would be quite an easy task. Since mean can be boosted by inflating the extreme values, the teacher might pick up the brightest students of the class (students who have already scored quite high), and improve their performance. For example, a student at 87% can be easily trained to perform at 100%. (while neglecting the weak students, as training them and expecting a good performance so as to boos the overall mean is a pretty time consuming task…and that too without a promise of success).

If on the other hand the teacher had been asked to raise the median by 20, then it would not have been easy. For the median to increase, the performance of at least half of the class needs to be improved. Half of the class has to score more than the set target.

In Customer satisfaction index, for example, it is better to focus on median than on mean.

So, median is a better representation of a set of data compared to mean.

Formula for median in Excel =median(a2:a12)

Formula for quartiles:

Q1 = Quartile(a2:12, 1)
Q2 = Quartile(a2:12, 2)
Q3 = Quartile(a2:12, 3)

Standard deviation gives a measure of dispersion (the extent to which values vary from the mean). Therefore standard deviation is a good measure for process performance rather than mean, median or mode.