# Bell Curve Generator

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In Statistics, a normal distribution is an important method used to get statistical information such as the mean or the standard deviation of the given set of data. Bell curve is the graph generated when data on the horizontal X-axis is plotted against amount of data on vertical Y-axis. Bell shaped curve is also called the Normal Distribution curve and is generated to analyze the given set of information.

Example 1: In a classroom, 68% of student’s weight are between 45kg and 65kg. Assuming this data is normally distributed, what are the mean and the standard deviation?

Mean can be calculated by taking the average of the maximum and the minimum numbers.

Mean = (45 + 65) / 2 = 110/2. So, Mean = 55kg
68% is 1 standard deviation on either side of the Mean.
So, 2 total standard deviations on the Bell curve!
This is the Empirical Rule.
Hence, 1 Standard Deviation = (65 – 45)/ 2 = 20/2 = 10
1 Standard Deviation = 10kg

Examples 2: In a classroom, 99.7% of the scores of an exam are between 76 and 94 points. Assuming this data is normally distributed, what are the mean and the standard deviation?

Mean can be calculated by taking the average of the maximum and the minimum numbers.
Mean = (94 + 76) / 2 = 170/2 = 85
Mean = 85points.
99.7% is 3 standard deviations on either side of the mean.
So, 6 total standard deviations. This is the Empirical Rule.

Hence, 1 Standard Deviation = (94 – 76)/6 = 18/6 = 3
1 Standard Deviation = 3points.