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Mean of Finite Numbers
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Mean

The mean is the average of the numbers, a numerical value that in some sense represents the central value of a set of numbers. To calculate the mean, just add up all the numbers, then divide by total number of numbers(count).
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Example: The mean of 20 numbers is 10. If 2 is added to every number, what will be the new mean ?
Solution: Let x1, x2, x3, x4 ... x20 be 20 numbers with their mean equal to 10. Then,

10 = (x1, x2, x3, x4, ... x20)/ 20
x1 + x2 + x3 + x4 + ... + x20 = 20 x 10 = 200 .....(i)
New numbers are x1 + 2, x2 + 2, x3 + 2, x4 + 2, ... x20 + 2
Let be the mean of new numbers. Then,
= [(x1 + 2) + (x2 + 2) + (x3 + 2) + (x4 + 2) + ... + (x20 + 2)] / 20
= [(x1 + x2 + x3 + x4 + ... + x20) + 2 x 20] / 20
= (200 + 40) / 20                           [Using equation (i)]
= 240 / 20 = 12
 
   
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