# Variance & Standard Deviation

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### Variance & Standard Deviation:

Variance & Standard Deviation By: Teri Smith

### What is Variance? :

What is Variance? The variance is the average of the Squared differences from the mean. To calculate the variance follow these steps: Work out the Mean (the simple average of the numbers) Then for each number: subtract the Mean and square the result (the squared difference ). Then work out the average of those squared differences.

### What is Standard Deviation :

What is Standard Deviation The Standard Deviation is a measure of how spread out the numbers are. Its symbol is σ (the greek letter sigma) The formula is easy: it is the square root of the Variance.

### Watch this video to find out how to calculate the Variance and Standard Deviation. :

Watch this video to find out how to calculate the Variance and Standard Deviation . https://www.youtube.com/watch?v=qqOyy_NjflU Or https://www.youtube.com/watch?v=Z85bxLADokw

### Here is another great example of how to find Standard Deviation :

Here is another great example of how to find Standard Deviation http://standard-deviation.appspot.com/ Or http://www.easycalculation.com/statistics/learn-standard-deviation.php

### Example: :

Example: The owner of the China Garden restaurant is interested in how much people spend at the restaurant. He examines 10 randomly selected receipts for parties of four and writes down the following data. 44, 50, 38, 96, 42, 47, 40, 39, 46, 50 He calculated the mean by adding and dividing by 10 to get 44+50+38+96+42+47+40+39+46+50=492 492/10=49.2 That is how you get the mean of 49.2

### Below is the table for getting the standard deviation: :

Below is the table for getting the standard deviation: x x - 49.2 (x - 49.2 ) 2 44 -5.2 27.04 50 0.8 0.64 38 11.2 125.44 96 46.8 2190.24 42 -7.2 51.84 47 -2.2 4.84 40 -9.2 84.64 39 -10.2 104.04 46 -3.2 10.24 50 0.8 10.24 Total 2600.4

### Example :

Example This is how you do the math for your table for Standard Deviation x=44 44-49.2=-5.2 (44-49.2) 2 =27.04 x x - 49.2 (x - 49.2 ) 2 44 -5.2 27.04

### PowerPoint Presentation:

2600.4 = 288.7 10 - 1 Hence the variance is 289 and the standard deviation is the square root of 289 = 17. Since the standard deviation can be thought of measuring how far the data values lie from the mean, we take the mean and move one standard deviation in either direction. The mean for this example was about 49.2 and the standard deviation was 17. We have: 49.2 - 17 = 32.2 and 49.2 + 17 = 66.2 What this means is that most of the patrons probably spend between \$32.20 and \$66.20. 