What is normal curve actually?

Hi All,

I am fairly new to Stats and thus this question.
I was going through different materials to learn stats.

1. Somwhere its mentiond that a population, if plotted against frequency on a bar graph can produce a normal curve (e.g popcorn popping, heights of people etc)
2. Whereas somewhere normal curve is associated with PDF, like its a function where you put infinite random continous variables and plot its probabilities to get a normal curve
3. Whereas somewhere its written that - use normal curve to take out out inferences out of sample data by using area under the curve and p values and z scores
4. Whereas somewhere its written that Binomial distribution follow normal curve when number os trials are huge in number
5. Whereas somewhere normal curve is assosciated with central limit theorem

Thus is it used for descriptive stats, or inferential stats? Thus I am not able to get my head around this, that what is a normal curve actually?
Request you to please answer as layman (english, without jargons) and detail as possible. this will help me get a clearer picture of it.

Many thanks in advance.
Last edited:


Well-Known Member
Hi Vibhor,

I will try to explain without the mathematical definition, but you will need to do it yourself so you will understand.
I generated for you 50 numbers that distribute normally (since 50 is a small number it won't look as perfect curve)

1. Please try to create a histogram for the below normal data.
Try each column with equal 1 (column1: -3 to -2, column2: -2 to -1, ...1 to2

2. Now do another similar histogram, but instead of frequency us for each column frequency/total number of values
(if for example, you get a column of 6 values now it should be 6/50.

Please show me your chars

"0.863275085241471, 0.416550704572538, 0.570703821446366, 0.504409324217315, 0.104365203863852, -1.06125636742907, -2.09258636524231, -2.63197389012965, -1.87012106019467, 0.0551535252557079, -0.0984356934733642, 0.926881528709935, -0.708933061141197, 0.16322878609733, -1.94941953183645, 0.398358723805098, 1.77655712714904, -0.3942174251198, 0.172172120846471, -0.0671904925509537, -0.0302644066744159, -0.441541000402508, -0.669576791848719, -0.0405475590425218, -1.04874575381918, 0.390819836777665, 1.53675069471934, -0.0981293561066762, -1.24880871197056, -0.378963348814644, -1.33245005969971, -1.79475185850679, -0.0167379919500286, 0.885890782801892, -0.276721194780797, -0.43863942775186, -0.228611504158969, 0.807811282377848, 1.16572571090321, -1.430000974997, 0.494163451031301, -0.722594657688781, 0.309193861201655, 1.45597395607195, 1.01744562837125, -0.675443010837308, 0.0828248931112463, 0.269828907282515, -1.45385589181604, 1.422952612358"