EXERCISE 6. AVERAGE
IMPORTANT FACTS AND FORMULAE
1. Average
= (sum of observations / number of observations)
2. 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 (2xy / X + y ) kmph.
SOLVED
EXAMPLES
Ex. 1. Find the average of all
prime number between 30 and 50.
Sol.
there are five prime numbers between 30 and 50.
They are 31,
37, 41 and 47.
Required
average = (31 + 37 + 41 + 43 + 47/5) = 199/5 =39. 8.
Ex. 2. Find the average
of first 40 natural numbers.
Sol. sum of first n natural numbers = n (n + a) / 2.
So, sum of
first 40 natural numbers = 40 x 41 /2 = 820.
Required
average = 820 / 40 = 20.5.
Ex.
3. Find the average of first 20 multiples of 7.
Sol.
required average = 7 ( 1 + 2 + 3 + ….. + 20 ) / 20 = ( 7 x 20 x 21 / 20 x 2) =
(147 / 2 ) = 73.5.
