How can we know that a series of data have a normal distribution?

Question

I have 4'000 data of railway track irregularities. I want to know that do they have normal distribution or not. how can I do that?

Answer 1

Before I go on with this, let me set the record straight; while most data will be Normal/Bell distributed, not all data will be. Arrival, queuing, and service times distribution are often if not usually Poisson or Erlang distributed, for example.

Now, having said that, data like irregularities (errors) are normally Normal. So, when all else fails, you can make a safe bet that your data are Normal/Bell distributed. But you can check your data to be sure. Here are some of the things you can do.

1. Calculate the average (mean--m) and standard deviation (sig) of a random sample (N>30 data points is usually sufficiently big) of your 4,000 data points population.. (See bottom of page on randomizing.)

2. Count the number of sample data points inside the 2 sig range (m - sig) --> (m + sig).

3. If approximately 2/3 of the sample data points lie inside the 2 sig range, and about 1/6 of the data points lie on either side of the 2 sig range, then your population (the 4,000 data points) is probably Normal. It least it will be close enough for Government work. Note, the 2/3 and 1/6 do not have to be exactly that, but reasonably close, say, not more than 10% off.

Randomizing: For your sample to be fair and represent the population (4,000 data points) it was drawn from, the sample data points have to be randomly selected. This simply means each one of the 4,000 data points in your population has to have equal probability of being selected when you draw your sample.

Excel has RAND, a function that can approximate random numbers. You can use it to draw your data points if you have numbered or lettered each data point in your population. Or you can buy an introductory statistics book that has a random number table in it. The table can be used to approximate a random number selection.

Answer 2

Too much ways can u do it.

but as statistical science you should try to get the variance or standard deviation.
It will give an indication about that .
another way is to draw the data histogram on excel as DATA VS Frequency. if the shape is like the bill or almost close. it will be considered as normal distribution.

but the best way is to take a samples from that data drawing the graph for at least 20 samples of data taken or according to your samples data quantity.
it is much easier.

Finally I'll tell u something that all large data quantities will be normally distributed. unless you have blunders in data collection.

Answer 3

You have to use the data to plot a graph.
If the shape of the graph looks like a 'bell' shap. It is a normal distribution.
In more mathematics terms, 85% of the distribution must be within 1 standard variation from the mean.

Answer 4

The above answers can be improved.

For a normal, you want mean and median to be nearly equal, skewness = (1/N)SUM(x^3)/(SD^3) to be close to zero, and kurtosis=(1/N)SUM(x^4)/(SD^4) to be close to 3.

There are more formal tests such as the Jarque-Bera statistic, but that is a little advanced.