How To Make a Normal Distribution Curve?

How do you make a distribution graph from the histogram? How is the normal distribution curve as well as the skewed curve so smooth? Many have the same questions in the mind. We shall try to get the answers to the same.

Many have you seen Bell curve, or a skewed curve in a statistics book. Many are yet to understand what that curve is and many are going ahead with confusion in the mind that what is it exactly and how did the author get the curve? As the name, it tells how the data are distributed around the central tendencies of the data set i.e. how many data and how they lay around the mean, median and mode of that data set. Just take for instance the following example of height of 30 students in a class.

Download the working file from the below –

Follow the steps as done in the excel sheet –

  1. Arrange the data in ascending order.
  2. Find the Mean, Median and Mode.
  3. Find the Standard Deviation
  4. Make a new X axis data for the graph to be –
    • From the Mean, take three value above it and three values above it. What values?
    • Mean – n*Standard Deviation, where n is the position of the number 1, 2 and 3. You get the values 115.25, 89.13, 63.
    • Similarly take three positions below the mean by using the formula – Mean + n*Standard Deviation, the values we get here are 167.51, 193.63 and 219.76
    • Arrange them in ascending order as shown – 63, 89.13, 115.25, 141.38, 167.51, 193.63 and 219.76
  5. For new Y series for the to be graph –
  • Count the no of values less than or equal to the first value of X-axis found in point 4 above, and mention it beside it. There are no height values below or equal to 63, so the Y-axis value will be zero.
    • Do the same for the rest of the values. We get the following table
 X axisY axis
(0, 63)63.000
(63, 89.13)89.130
(89.13, 115.25)115.255
(115.25, 141.38)141.3812
(141.38, 167.51)167.516
(167.51, 193.63)193.636
(193.63, 219.76)219.761

6. Draw the graph, and we get something like this

Distribution Curve

What you see from the above right skewed graph, is it not similar to the skewed bell curve? Wait but where is the smooth lines, here it is full of kinks.

You see many graphs from various authors and other places similar to below curve shown in Black. This happens by the process called smoothing.

Hand Drawn Smoothing Curve

Smoothing itself is a big process and more the data you have the better and smooth curve you may get. You can know how smoothing is done by clicking here and here

You can read about Normal distribution and Skewed curve from here