Question

How do you find the standard deviation of 3, 7, 4, 6, and 5?

Answer 1

The standard deviation is `sigma=sqrt(2) ~~1.41`

Explanation:

The standard deviation of a data set is given as:

`sigma=sqrt(1/NxxSigma_{i=1}^N(x_i-bar(x))^2)`

where:
`N`- number of data;
`bar(x)` - mean value;
`x_i` - data in data set

To calculate the deviation we can use the following algorythm:

1. Calculate mean `bar(x)`
2. Calculate `(x_i-bar(x))^2` for all `i`
3. Add all values calculated in `2`.
4. Divide the sum by `N`
5. Get square root to calculate the deviation.

Here we have:

1. `bar(x)=(3+4+5+6+7)/5=25/5=5`
2. `(3-5)^2=(-2)^2=4`
   `(4-5)^2=(-1)^2=1`
   `(5-5)^2=0`
   `(6-5)^2=1^2=1`
   `(7-5)^2=2^2=4`
3. Sum is `4+1+0+1+4=10`
4. `10-:5=2`
5. `sigma=sqrt(2)~~1.41`