Central Tendency

Posted on November 17, 2009 by


How much time has Carl been spending test driving different cars? When describing the data collected on a given variable, whether it be a Six Sigma or other type of study, a measure of central tendency is often reported. The Mean, Median, and Mode are all measures of central tendency. Here is an example: Carl took 10 cars for a test drive and this is how many minutes he spent driving each of the 10 cars: 5, 10, 10, 10, 11, 12, 15, 15, 16, and 18.

The mean (average) is calculated by adding these 10 numbers and then dividing that sum by 10 since that is how many test drives he took. The sum of these numbers is 122 minutes. Divide this by 10 to obtain the mean, and the answer is that 12.2 minutes were spent on average with each car.

The Median is the number in the middle of the distribution. The numbers are first sorted as they are above from smallest to largest, and the number found in the exact middle is the median. Since we have an even number of observations in this case (10 test drives) there are two numbers in the middle—11 and 12. Because there are two numbers in the middle, the Median is what number would be right in-between those two numbers. This can be found by taking the mean of these two middle numbers. So 11 + 12 = 23 which when divided by 2 is 11.5. So the Median is 11.5.  

The Mode is simply the most frequent number. In this case, three cars were driven for 10 minutes, which is the most frequent number in this distribution, so the Mode is 10.

Posted in: Six Sigma