Normal distribution > Normal or not?
1234Normal or not?

Theory

If you take a normally distributed variable X with expectation μ ( X ) and standard deviation σ ( X ) and use normal probability plotting paper to plot the probabilities Ρ ( X g ) against g, then you will get a straight line: on normal probability plotting paper, every true normal distribution will become a straight line.

If you transform your given frequency distribution into a cumulative frequency distribution and plot the values on normal probability plotting paper, then you should get a straight line if the frequencies are distributed normally. Make sure to plot the cumulative relative frequencies against the upper bounds of the classes!
Use the following link for a sheet of normal probability plotting paper: Normal probability plotting paper

You often find that the points of the cumulative relative frequency distribution do not precisely lie on a straight line on normal probability plotting paper. You then draw a line that fits the points as closely as possible. In effect you approximate your frequency distribution by a normal distribution corresponding to the line.
You can then find an estimate for the expectation by reading off the value corresponding to 50% on the line. Also, since one of the rules of thumb states that in a normal distribution 68% of observations are found in the interval [ μ σ , μ + σ ] , you can use the 84% point of the line to determine the value of μ + σ .

previous | next