MEASURE OF DISPERSION PART 2

Objectives: 

1. The meaning of Standard Variation 

2. Measure of tendency(average) 

3. Standard deviation is linked to the mean

What is the meaning of Standard Variation?

Standard Variation is a method of measure of how spread out numbers are. 

"What is variance?" 

Definition - The average of the squared differences from the mean. 

To find Variance...

You must follow this steps:

1. Find the mean 

2. Find the deviation from the mean

3. Square the deviation from the mean 

4. Find the sum of the squares 

5. Divide the sum of the squares by the number of items 

There are two ways of finding variance 

If small data or a sample

if big data or a population

After finding variance, now we can find the standard deviation. How to find standard deviation? We just find the square root of the variance.

Let's take an example...

Example 1

Example 2 

What is the population standard deviation for the numbers : 75, 83, 96, 100, 121 and 125? 

Example 3 

A booklet has 12 pages with the following numbers of words : 

271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 and 314

What is the standard deviation number of words per page? 

lets take an exercise...

Nine friends each guessed the number of marbles jar. 

When the answer was revealed they found they had guessed well (and one was the winner) 

Here is how the close they each got : 

-9, -7, -4, -1, 0, 2, 7, 9, 12 

(A negative number shows an underestimate, a positive number shows an overestimate) 

what was the standard deviation of their errors?