Tutorial

In the field of aptitude, Average is defined as the sum of numbers divided by number of elements that are being averaged.

For example, if there are ‘n’ numbers in a series {1, 2, 3, 4, 5, 6, … , n}, then, their average is given as :

[math]
\boxed
{
average \;=\; \frac{(1\;+ \;2\; +\; 3\; +\; 4 \;+\; …\; upto \;n\; terms)}{n}
}
[/math]

For example, average of first 5 numbers is :

[math]
average \;=\; \frac{(1\;+ \;2\; +\; 3\; +\; 4 \;+\; 5)}{5}
[/math]

[math]
average \;= \; 3
[/math]

In other words, average can also be expressed as :

[math]
\boxed
{
average \;= \;\frac{(sum \;of\;observations)}{(total\;observations)}
}
[/math]

Average Speed

In the field of aptitude, average speed is defined as the ratio of total distance to the total time.

[math]
\boxed
{
average \;speed\;= \;\frac{(total\;distance)}{(total\;time)}
}
[/math]

If a person travels some distance at a speed of x km/hr and the same distance at a speed of y km/hr, then the average speed during the whole journey is given as :

[math]
\boxed
{
average \;speed\;= \;\frac{2\;*\;x\;*\;y}{(x\;+\; y)}
}
[/math]

If a person covers a km at x km/hr and b km at y km/hr and c km at z km/hr, then the average speed in covering the whole distance is given as :

[math]
\boxed
{
average \;speed\;= \;\frac{(a\;+\;b\;+\;c)}{(\frac{a}{x}\;+\;\frac{b}{y}\;+\;\frac{c}{z}\;)}
}
[/math]