In statistics, there are many pattern in which a data can be distributed over a graph. It can be distributed more towards the left or can be distributed more towards right. Sometimes, the data is all mixed up. If the data, when graphically represented, shows a bell-shaped curve, the data is said to be normally distributed. The normal distribution is also referred as Gaussian distribution and belongs to the family of continuous distributions.
The graph of normal distribution has a single peak position which is located exactly at the center. The central point represents mean, median and mode. For normally distributed data, mean, median and mode are same. There are fifty percent of the data lies at left side and fifty percent on the right of the central position. The standard deviation of the data decides the spread of the distribution. The larger the standard deviation, the more the data is spread around the central position. Similarly, the smaller the standard deviation, the lesser the data is spread around the central position.
Therefore, the shape of curve depends upon the mean and standard deviation of the distribution. In the graphs shown below, left-side curve on the left is wider and shorter than that on the right, since left curve has smaller mean and bigger standard deviation.
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