This data represents the number of books Sarah reads each month:

Question

{ 1, 1,3,3,4}

 

What is the approximate standard deviation of the data set?

 

A) 1.2

B) 2.4

Answer 1

The variance is the mean of the squared differences ....

To find the variance we divide by n

The sum of the squared differences from Lincoln's work is  7.2

The mean of the squared differences is 7.2/5 = 1.44

This is the variance...

To find the standard deviation take the square root of the variance

√1.44 = 1.2

 

Answer 2

The standard deviation is defined as the sum of the differences between each data point and the mean squared all divided by one less than the total number of data points. Thus,

 

mean = (1+1+3+3+4)/5=12/5 or 2.4

standard deviation = ((1-2.4)^2 + (1-2.4)^2 + (3-2.4)^2 + (3-2.4)^2 + (4-2.4)^2)/(5-1) = 1.8

 

Are there other possible answers than those provided in A and B?