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Normal Distribution

What is Normal distribution? 
Data can be generally spread in different ways that can be either spread to the right or left but there exist many cases where the data tend to exist around some central value which tends it to take some bell -shaped curve. It is called the normal distribution.

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Examples for the normal distribution includes,

  1. Blood pressure readings.
  2. Marks scored on the test.

Characteristics of Normal distribution
Generally,

  • Mean = Median =Mode
  • Symmetry usually lies in the centre.
  • Simply it can be explained as 50% of the values are usually less than the mean and 50% are greater than the mean.
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Parameters of Normal distribution
Mean
Mean can be generally defined as the central tendency of the distribution. It generally defines the location for the peak value of the normal distribution.

Standard Deviation
It is generally used to determine how far from the mean the values tend to spread on either side.

Empirical Rule for Standard Deviation
For any of the following normally distributed data,

  • 68% of the data usually falls within 1 standard deviation of the mean.
  • 95% of the data usually falls within 2 standard deviations.
  • 99.7% of the data falls between 3 standard deviations.

Standardizing the Standard Normal distribution
Any of the normally distributed data can be converted to the standard form using the below formula,
Z = (x-µ)/σ.
X – Represents the raw value of the measurement.
µ and σ are generally the parameters of the population.
Generally, the values in the x scale are the actual values and the z scale is the standardized values.

Example:
Let us see if the mean and standard deviations are given how to convert it to the Z-Score.
A survey of daily walking time has these minutes,
26, 33, 65, 28, 34
The mean is given by 38.8 and the standard deviations are given by 11.4.
Let’s find the z-score

Original valueCalculationZ-score
26(26-38.8)/11.4-1.12
33(33-38.8)/11.4-0.51
65(65-38.8)/11.42.30
28(28-38.8)/11.4-0.94
34(34-38.8)/11.4-0.421

Reference

https://www.investopedia.com/terms/n/normaldistribution.asp#:~:text=A%20normal%20distribution%20is%20the,all%20symmetrical%20distributions%20are%20normal.

https://www.mathsisfun.com/data/standard-normal-distribution.html

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