Standard Deviations

Standard deviation is a numerical value that represents the extent of variability or dispersion among a set of data. A high value of standard deviation indicates that the spread of a set of data around the mean or average value is more. A low standard deviation value means the data values are closely clustered around the mean value. It is important to note that the mean value of two different data sets can be the same but the dispersion of data values of both sets can be different. So we can say, different data sets can have the same mean value but different standard deviations.

In mathematical calculation particularly in statistics, the concept of standard deviation is very useful to find out how the data is spread out around the average value. It indicates whether most of the observations are close to the mean or many data values are far above or far below the mean value. Standard deviation refers to the variation of each data point from the mean or average value. When all the values of a set of data are close to the mean value, the standard deviation is less as compared to the data set that has values farther away from the mean.

For example, we can take two sets of data. The first one is 27, 13, 12, 8, and 25. The second set is 15, 18, 15, 20, and 20.

Here, both the data sets have the same mean which is 17. But it is observed the first set of values is more close to the mean value while the second set of data values is widely spread.

How to Denote Standard Deviation

The process used to express the standard deviation of a set of data in numerical form is as follows:

  1. Calculate the average or arithmetic mean of the set of given data values.
  2. Subtract the mean value from each of the data values and square the result for each data.
  3. Add all the squared values and the sum is divided by the number of observations.
  4. Find the square root of the result obtained in step 3 which gives the value of standard deviation.


Statistics is the subject that is related to the collection, organization, analysis, interpretation, and presentation of different types of data available to us. There can be a large amount of data available that needs to be organized and analyzed to convert it to some useful information that can be applied in many fields for theoretical and practical purposes. There are useful applications of statistics in the interpretation of information in scientific, industrial, or social fields. It is a conventional method to start with a sample of the population and apply statistical tools to represent the property of the sample.

Statistics helps to use the proper methods to collect the data, apply the correct analysis process, and present the results for effective interpretation. Data are a very important part of statistical analysis that represents the facts and figures that need to be summarized. These are the observations that can be in the form of numbers, measurements, or statements. Data can be of two types, quantitative and qualitative. Quantitative data are measurable like how much or how many of something, and qualitative data provide names, categories, or other characteristics of data. Statistics is concerned with the application of the right methods to analyze sample data from a population to reflect certain patterns and trends.

The application of statistics is found in various scientific fields and research areas that deal with situations in which we have to follow the trends or specific properties of data to arrive at probable outcomes. Statistics also help to understand and control the sources of variation in the data and analyze accordingly to present a meaningful inference.

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