[latex] \mathbf{ Average = \left ( \frac{Sum \: of \: observation}{Number\: of\: observation } \right )} [/latex]

Suppose a man covers a certain distance at x kmph and an equal distance at y kmph. Then, the average speed during the whole journey is [latex] { \left ( \frac{ 2xy }{ x+y } \right )} [/latex] Kmph. 

This basic formula for the average  of numbers x1, x2, x3, …. xn

An = ( x1 + x2 + x3 + …….. + xn)/n = ( Total of set of n numbers)/n

This also ‘means An*  n = total of the set numbers.

When we have two or more groups whose individual averages are known, then to find the combined averages of all the elements of all the groups we use weighted averages. Thus, if we have K groups with averages A1, A2, …… Aand having n1, n2, ….., nk elements then the weighted averages are given by the formula: 

[latex] A_{w} = \frac{n_{1}A_{1} + n_{2}A_{2}\,+\,n_{3}A_{3} \, +\cdot \cdot \cdot \cdot \cdot n_{k}A_{k} }{n_{1}\, +\,n_{2} \,+\,n_{3}\, +\cdot \cdot \cdot + n_{k} } [/latex]


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