Application of Statistics in Textile Testing

Measurement of Central Tendency

A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. As such, measures of central tendency are  sometime called measures of central location. They are also classed as summary statistics. The mean (often called the average) is most likely the measure of central tendency that you are most familiar with, but there are others, such as the median and the mode.

Mean

The mean (or average) is the most popular and well known measure of central tendency. It can be used with both discrete and continuous data, although its use is most often with continuous data. The mean is equal to the sum of all the values in the data set divided by the number of values in the data set. So, if we have n values in a data set and they have values X ₁,X₂,..........,Xn  the sample mean, usually denoted by  x̄ (pronounced X bar) 

 

This formula is usually written in a slightly different manner using Greek capitol letter, ∑ , pronounced "Sigma" which means "sum of "

∑X / n

You may have noticed that the above formula refers to the sample mean. So, why have we called it a sample mean? This is because, in statistics, samples and population have very different meanings and these differences are very important, even if the case of the mean, they are calculated in the same way. To acknowledge that we are calculating the population mean and not the sample mean, we use the Greek lower case letter "mu", denoted as µ

µ = ∑X / n