## Mean, Standard Deviation & Variance

##### Enter all numbers separated by comma ","
e.g 4,5,65,34

 Results Total Numbers 0 Mean(Average) 0 Standard Deviation 0 Variance 0 Population Standard Deviation 0 Population Variance 0

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# Mean, Standard Deviation, Variance, Population deviation

Statistic is a very important concept of math which deals with collection, organization, analysis and interpretation of small to large number of data. For these very reasons mean, median, mode, range, standard deviation , variance, and population deviation becomes the building blocks. They hold the framework for rest of the calculations. Below is a short description of mean, standard deviation, variance and population deviation.

• Mean – Average value
• Standard deviation – measure of variability or diversity of a set of number
• Median – Midpoint between lowest and highest value of a set
• Range – Difference between largest and smallest value within a set

Below are more detailed explanation of Mean, Standard Deviation, Population Deviation and Variance.

Mean:

What is mean? Mean has various synonyms such as statistical mean and arithmetic mean which is simply the average of a set or sample of numbers.  For a set of number, the mean is the sum of all the values divided by number of values.  The mean of set of numbers usually denoted by “x bar” or x .

Example:
Q1:   What is the mean for the set 34, 28, 50, 25, 8.

Ans:   The formula for mean is

Mean = (34+28+50+25+8)/5
Mean = 145/5 = 29

Standard Deviation:

Standard deviation is rather a step up concept from mean. Standard deviation calculates the average spread of data from its mean. It allows for understanding normal distribution. Normal distribution means most of the variables in a set of data are close to their mean while only few are extreme apart. Standard deviation tells us how tightly all the number are clustered to mean. A small standard deviation means that the values are close to their mean where a large standard deviation indicates a large spread of values from their mean. Along with understanding variability, standard deviation is also used to measure statistical conclusion such as margin of error and confidence interval. Althought he standard deviation formulas look scary at the bottom. It is quite easy if we approach it the right way. Below is example of standard deviation and how to calculate it properly. However, you can always use the

Variance:

Variance is described as statistical measure of how far from expected values a set of values are. Meaning how far a set of numbers are spread out from their mean. In another word, Variance is a measure of variability. Variance is typically denoted with Var(X) ariance is squared value of Standard Deviation.
Variance is the square value of Standard Deviation.

Variance = S2

Though the formula for calculating standard deviation seems scary, there is a systematic way to calculate. Use the Standard Deviation Calculator above to calculate standard deviation. The steps to calculate Standard Deviation and populations are below.

Steps to Calculating Standard and Population Deviation:

Find the standard deviation  for 2, 3, 6, 5, 8.

Step1:      First we need to find the Mean
(2 + 3 + 6 + 5 + 8)/5 = 4.8

Step 2:     2nd build the chart below

Step 3:    3rd find the sum of all (X-X)2
7.84 + 3.24 + 1.44 + 0.04 + 10.24 = 22.8

Step 4:    Find the total number of elements. 5 – 1 = 4

Step 5:    Find the standard deviation.

Sqrt(22.8/4) = 2.39

Step 6: To find the popular deviation use the whole number which is 5.

Sqrt(22.8/5) = 2.14

Steps to calculate variance:

Find the standard deviation  for 2, 3, 6, 5, 8.

Step 1:    Find the mean of the set

(2+3+6+5+8)/5 = 4.8

Step 2:    Subtract the mean from each value and squre the result

(2 - 4.8)2 + (3 - 4.8)2 + (6 - 4.8)2 + (5 - 4.8)2 + (8 - 4.8)2 = 22.8

Step 3:    Divide the sum by the number of values in the set.

22.8/5 = 4.56

Step 4:    However, the true Variance from Standard Deviation is (2.39) 2 = 5.7.

Suggested Calculators:

Mean, Median, Mode, Range Calculator