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The usual definition of the Standard Deviation of a Frequency table is

An easier definition that avoids finding (x-) is as follows

That is the standard deviation is the square root of the mean of the squares of the information – the square of the mean.

This method is often a lot easier to use that the standard definition.

Leaving Cert higher maths 1995.

Find the mean and standard deviation of 0,x, 1

The mean is . Now find the Standard Deviation using

Show

Show that the minimum value of the minimum occurs when dy/dx = 0

Leaving Cert Maths (H) 1999.

If the mean of a, 3a,b, 2b is 2b. (i) Write b in terms of a.(2) find the mean and standard deviation in terms of a. The mean is

In the last part we are asked to solve

Leaving Cert Higher Maths 1997.

The mean of the data {1,2,5,x, y} is 5.

Find in terms of x (i) y and (ii) the standard Deviation.

The mean is

The Standard deviation squared is

An Interesting Example

If have as their mean and standard Deviation .

Find the mean and Standard Deviation of

Solution : The mean is

The Standard Deviation squared is

Remember that