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Normal Distribution or Skewed?

Normal Distribution is one of the important concept in statistics. It not only helps you to visualize the property of your data, but also guides you in how to treat it. Let us take a look from the practical aspects.

What is normal distribution? What if the data is not normally distributed? Do you have any idea if your data is skewed and not normally distributed? What will be the central tendency if Normal distribution is not present in your data?

Data Distribution Study

There are several terms associated with identification of the data set, mostly through the measure of central tendencies. By knowing those values, you can link the data set with the appropriate measures of central tendencies. There are fewer chances to get a perfect normal distribution curve out of a data set in the real world. So, it is advisable to know more about the type of data you have, i.e. to know about the skewedness of the data. In few of my previous blogs you must have seen data sets where Mean, Median and Mode are not same i.e. there is skewedness in the data set. In case you have not read then click here

How does knowing of skewedness of your data helps you?

  • Helps you to know which measure of central tendency to use for that data. You know from my previous blogs that Average is not always the indicator of your data set.
  • Helps you to know which portion is major contributor to your data set. If someone is selling say 12 no of items in his business. He wants to check which product out of the 12 is bringing maximum than others combined. We will see more in coming examples.
  • To know if your data is biased because of over concentration of data from one side in your total data set.

If you know at least the above, you can work on your data set again to rectify the mistake in data collection and collect correct and relevant data or at least reduce the level of skewedness.

Normal Distribution

Normal distribution is a bell curve, which means Mean, Median and Mode is same and at the top of the curve. Which also tells that –

  • Data is distributed evenly.
  • Equally distributed of data on both side of the mean
  • Non-biasedness of the data

Let us see an example regarding Normal Distribution, download the working file below

A group of 16 children were given a fruit, data is available in the excel sheet. This distribution is Normal

A group of 16 children were given a fruit, data is available in the excel sheet. This distribution is Normal
Normal Distribution

However, before concluding the same, one must make sure that extreme values on either side of the mean are not affecting the data set. Because these extreme values or outliers can nullify the skewedness of the main data set.

If the data set is skewed, then the values of the Mean, Median and Mode will not be equal. The two type of skewedness is Right Skewed and Left Skewed data.

Right Skewed Distribution

Right Skewed – The common character of these type of data set is Mean>Median>Mode.

  • The Data is not evenly distributed.
  • Inside the data set, there are data value which is high and maybe more in number
  • The tail to the right side of the deformed bell curve is longer as compared to that on the left side. The left tail seems to have been cut short as seen in the following picture

Let us see an example through the same child and fruit example, now with change in some figures, refer to the excel sheet. When you get the graph, you see that the right leg is more stretched than the left side.

Let us see an example of Right Skewed distribution through the same child and fruit example, now with change in some figures, refer to the excel sheet. When you get the graph, you see that the right leg is more stretched than the left side.
Right Skewed

Left Skewed Distribution

Left Skewed – The main character of this kind of data set is Mean<Median<Mode. Other characters are similar to the Right skewed, but everything is left here. You can refer to the example in the excel sheet.

Let us see an example of left skewed distribution through the same child and fruit example, now with change in some figures, refer to the excel sheet. When you get the graph, you see that the right leg is more stretched than the left side.
Left Skewed

The red lines inside the graphs are smoothing effect  line curve drawn by hand for understanding of how the bell curve looks. To know how bell curve is drawn, please click here to read the next blog.