Explanation Definition: Standard deviation: Suppose x is a data value in a set whose mean is x ¯ , then x − x ¯ is called x ’s deviation from mean. The formula for standard deviation of a sample n data values is s = ∑ ( x − x ¯ ) 2 n − 1 . Mean: Suppose the data set contains n data values, the mean x ¯ of the data is computing by the formula x ¯ = ∑ x n . Calculation: Standard deviation is a reliable measure of dispersion. It is a number and used to tell about the measurements for a group of data. That is the spread out from the average value or mean or expected value by using the definition mentioned above. The low standard deviation denotes that most of the numbers are close to the average. The high standard deviation denotes that the numbers are more spread out. Example: The given distribution is 8 , 6 , 7 , 6 , 4 , 5 . Compute the mean for the distribution 8 , 6 , 7 , 6 , 4 , 5 . Here, n = 8 . Compute the mean of the distribution by using the mean formula mentioned above. x ¯ = 8 + 6 + 7 + 6 + 4 + 5 8 = 36 6 = 6 Therefore, the mean of the distribution is x ¯ = 6 . Compute the squares of the deviations of the data values from the mean as shown in below table

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Author: Pirnot

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To explain:

The standard deviation tells about a distribution.