# Standard Deviation - (Jan/05/2009 )

Hey,

I need to determine the standard deviation of some numbers for a biology report.

Does anyone know any websites with a step by step example of calculating standard deviation. I've had trouble finding anything for people who aren't good at math.

Thanks.

Why not just go ahead with EXCEL sheet???

I would have to say that Excel is terrible for all things statistical... proper stats software is definitely the way to go.

Anyway to answer the OP:

From wikipedia:

1. Find the mean of the values.

2. For each value (xi) calculate its deviation from the mean (xi - mean).

3. Calculate the squares of these deviations.

4. Find the mean of the squared deviations. This quantity is the variance σ2.

5. Take the square root of the variance.

The standard deviation of a data set is the same as that of a discrete random variable that can assume precisely the values from the data set, where the point mass for each value is proportional to its multiplicity in the data set.

[edit] Example

Suppose we wished to find the standard deviation of the data set consisting of the values 3, 7, 7, and 19.

Step 1: find the arithmetic mean (average) of 3, 7, 7, and 19,

(3 + 7 + 7 + 19) / 4 = 9.

Step 2: find the deviation of each number from the mean,

3 − 9 = − 6

7 − 9 = − 2

7 − 9 = − 2

19 − 9 = 10.

Step 3: square each of the deviations, which amplifies large deviations and makes negative values positive,

( − 6)^{2} = 36

( − 2)^{2}= 4

( − 2)^{2} = 4

10^{2} = 100.

Step 4: find the mean of those squared deviations,

(36 + 4 + 4 + 100) / 4 = 36.

Step 5: take the non-negative square root of the quotient (converting squared units back to regular units),

\sqrt{36} = 6

So, the standard deviation of the set is 6. This example also shows that, in general, the standard deviation is different from the mean absolute deviation (which is 5 in this example).

Note that if the above data set represented only a sample from a greater population, a modified standard deviation would be calculated (explained below) to estimate the population standard deviation, which would give 6.93 for this example.