### What is Average?

The result obtained by adding several quantities together and then dividing this total by the number of quantities is called Average.

Average = *Sum of all observation *number of observation

The mean of n observation a_{1}, a_{2}, a_{3}………… a_{n} is given by

= *a _{1} + a_{2} + a_{3} +…………+ a_{n}*n

Where the symbol ∑ called sigma which stands for summation.

### Properties of Average

When the difference between all the items is same (and the number of terms is odd), then the average is equal to the middle term.

If x is added to all the items, then the average increases by x.

If x is subtracted from all the items, then the average decreases by x.

If every item is multiplied by x, then the average also gets multiplied by x.

If every item is divided by x, then the average also gets divided by x.

Average formula for An AP Series= (1st term + last term)/2

### Problem Related to this topic

**1.) Find the mean driving speed for 6 different bikes.**

66 km/h, 57 km/h, 71 km/h, 54 km/h, 69 km/h, 58 km/h

**Solution**: number of observation = 6

Average = *Sum of all observation *number of observation

= *66 + 57 + 71 + 54 + 69 + 58*6

= *375*6

= 62.5 km/h

**2.) If average of two numbers is 77.5 and a number is 5.5 less than the average, then what is the second number?**

**Solution**:

From this formula

Average =

*Sum of all observation*number of observation

Sum of all observation = Average x number of observation

=77.5 x 2 = 155

=77.5 – 5.5 = 72

second number is ( 155 – 72 ) = 83

**3.) The average run of a cricket player of 8 innings was 34. How many runs must he make in his next innings so as to increase his average of runs by 6?**

**Solution**:

**Step 1:**Average run of a player in next innings is 9 = (34 + 6) = 40 runs.

**Step 2:** Required run for 9 innings is (40 x 9) = 360 runs and 8 innings is

(34 x 8) = 272 runs.

So, required number of run is = (360 – 272) = 88 runs.

**4.) In a shop out of 9 persons, 8 persons spent Rs. 30 each for their shopping. The ninth one person spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them.**

**Solution**:

Let the average money spent be Rs. x, Then

9x = 8 x 30 + (x + 20 )

9x = x + 260

8x = 260

x = 32.50.

Total money spent by = 9x = 9 x 32.50 = 292.50.

**5.) The average age of 15 boys is 18 years in the Math’s class and that of 13 girls is ages 15 years. What is the average age of total math’s class?**

**Solution**:

In a math’s class 15 boys ages 18 years = ( 15 x 18 ) = 270

In a math’s class 13 girls ages 15 years = ( 13 x 15 ) = 195

**Average =**

*Sum of all observation*number of observationSo average age of total math’s class is =

*270 + 195*15 + 13 =

*465*28

16.607.

**6.) Four years ago, the average age of Rajesh and Suresh was 16 years. With Dipika joining them, the average age becomes 24 years. How old Dipika now?**

**Solution**:

Present age of (Ramesh + Suresh) = ( 16 x 2 + 4 x 2 ) = 40 years.

Present age of (Ramesh + Suresh + Dipika) = (24 x 3) = 72.

Dipika present age is (72 – 40) = 32.

**7.) The average monthly income of A and B is Rs.6040. The monthly average income of B and C is Rs.7500 and monthly average income of A and C is Rs. 6500. Find the income of A in a monthly**

income?

income?

**Solution**:

**Step 1:**here is ABC given respectively monthly income, hence we need

to find both income.

(A + B) = (6040 x 2) = 12080, (B + C) = (7500 x 2) = 15000, (C + A) = (6500

x 2) = 13000

**Step 2:** If we add 3 income 2( A + B + C ) = 2 x ( 12080 + 15000 + 13000 )

= 40080 or A + B + C = 40080 / 2 = 20040.

**Step 3:** So we get the income of A Subtract income of (A + B + C) – (B +

C) = (20040 – 15000) =5040.5

**8.) The average of five numbers is 62. The average of the second and the third number is 45. The average of the first and the fifth number is 66. What is the fourth number?**

**Solution**:

Average of Five numbers is = 62 x 5 = 310

Average of second and third number = 45 x 2 = 90

Average of first and fourth number = 66 x 2 = 132

( 132 + 90 ) = 222

The fourth number is ( 310 – 222 ) = 88

**9.) In a school of class x after replacing an old student by new student, it was found that the average age of eight students of class x is the same as it was 5 years ago. What is the difference between the ages of the replaced and new students?**

**Solution**:

Age decreased = (8 x 5) = 40 years.

So the required age difference is = 40 years.

I hope, this article will help you a lot to understand the **Average | Formulas | Properties | Examples**. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.