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

##### 1 Answer

Dec 19, 2016

The standard deviation is

#### Explanation:

The standard deviation of a data set is given as:

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

where:

To calculate the deviation we can use the following algorythm:

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

Here we have:

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