Standard Deviation Example

Standard Deviation Example Standard Deviation Example Standard Deviation is used to measure the deviation of data from its mean. It is equals to square root of variance; standard deviation tells us that how many data items are distributed above and below the mean.

The formula is for standard deviation is: S = √∑(x – x’2) N–1 Where s = the standard deviation X = each value in the sample X’ = the mean of the values N = the number of the values (the simple size)

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For finding the standard deviation we follow some steps which are given below: Step 1: For finding the standard deviation first we have to find the mean of the given data.

Step 2: After doing so subtract mean value from each value present in data set.

Step 3: Find the assumed mean of values we got in step 2.

Step 4: Then find the square root of value we got from step 3, the value we get now is the standard deviation.

Suppose the amount of gold coin 5 pirates has 7, 6, 4, 8, and 10 respectively, we can calculate the standard deviation of amount of gold coins as shown below: We know that the formula for standard deviation is: S = √∑(x – x’2) N–1 Here the value of‘s’ is the standard deviation, and ‘x’ is each value in the sample, and x’ is the mean of the values, and ‘N’ is the number of the values. For finding the standard deviation we have to follow above steps so that it is easy to find the standard deviation.

First we calculate the mean of the given data, and the formula for the finding the mean is: X’ = ∑x, N

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or X’

= x1+ x2+ x3 + x4 …. + xN, N = 7 + 6 + 4 + 8 + 10; 5 = 35 5 = 7;

So the mean value is 7; Now we calculate x – x’ from the given data: X1 – x = 7 – 7 = 0, X2 – x = 6 – 7 = -1, X3 – x = 4 – 7 = -3, X4 – x = 8 – 7 = 1, X5 – x = 10 – 7 = 3, Now we have to calculate ∑(X1 – x)2; ∑(X1 – x)2 = (X1 – x)2 + (X2 – x)2 +… (Xn – x)2, = (0)2 + (-1)2 + (-3)2 + (1)2 + (3)2,

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