**Worksheet on Average :**

Worksheet given in this section is much useful to the students who would like to practice problems on average.

**Problem 1 :**

Find the average of first 20 natural numbers.

**Problem 2 :**

Find the average of first 15 odd numbers.

**Problem 3 : **

Find the average of first 20 natural numbers which are divisible by 7.

**Problem 4 :**

The average of four consecutive even numbers is 27. Find the largest of these numbers.

**Problem 5 : **

There are two sections A and B of a class, consisting 36 and 44 students respectively. If the average weight of the section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class.

**Problem 1 :**

Find the average of first 20 natural numbers.

**Solution : **

**Step 1 :**

Write the formula to find sum of first "n" natural numbers.

S_{n} = n(n+1) / 2

**Step 2 :**

Use the formula given in step 1 to find the sum of first 20 natural numbers.

S_{20} = 20(20+1) / 2

S_{20} = 20 ⋅ 21 / 2

S_{20} = 210

**Step 3 :**

Find the average of first 20 natural numbers.

Average of first 20 natural numbers is

= Sum of first 20 natural numbers / 20

= 210 / 20

= 10.5

Hence, the average of 20 natural numbers is 10.5

**Problem 2 :**

Find the average of first 15 odd numbers.

**Solution : **

**Step 1 :**

Write the formula to find sum of first "n" odd numbers.

S_{n} = n^{2}

**Step 2 :**

Use the formula given in step 1 to find the sum of first 15 odd numbers.

S_{n} = n^{2}

S_{15} = 15^{2}

S_{15} = 225

**Step 3 :**

Find the average of first 15 odd numbers.

Average of first 15 odd numbers is

= Sum of first 15 odd numbers / 15

= 225 / 15

= 15

Hence, the average of 15 odd numbers is 15.

**Problem 3 : **

Find the average of first 20 natural numbers which are divisible by 7.

**Solution : **

**Step 1 :**

The first natural number which is divisible by 7 is 7.

The next numbers which are divisible by 7 are 14, 21..... **Step 2 :**

Write the first twenty natural numbers which are divisible by 7.

They are 7,14,21,28........ up to 20 terms. **Step 3 :**

Find the sum of all the above numbers.

= 7+14+21+28.........up t0 20 term

Because all of the above numbers are divisible by 7, we can factor 7.

= 7(1+2+3+4+.........+20)

Therefore, sum = 7(210)

**Step 4 : **

Find the average.

Average = (sum of all 20 numbers)/20

Average = (7⋅210)/20

Average = 73.5

Hence average of first 20 natural numbers which are divisible by 7 is 73.5

**Problem 4 :**

The average of four consecutive even numbers is 27. Find the largest of these numbers.

**Solution : **

**Step 1 :**

Let "x' be the first even number.

Then the four consecutive even numbers are

x, x+2, x+4, x+6.

**Step 2 :**

Average of the four consecutive even numbers = 27

So, we have

(x+x+2+x+4+x+6) / 4 = 27

(4x + 12) = 108

4x = 96 ===> x = 24

Hence the largest even number = (x + 6) = 30.

**Problem 5 : **

There are two sections A and B of a class, consisting 36 and 44 students respectively. If the average weight of the section A is 40 kg and that of section B is 35 kg, find the average weight of the whole class.

**Solution : **

**Step 1 :**

For section A, average weight = 40 kg.

That is,

(sum of the weights of 36 students) / 36 = 40

Sum of the weights of 36 students = 1440.

**Step 2 :**

For section B, average weight = 35 kg.

That is,

(sum of the weights of 44 students) / 44 = 35

Sum of the weights of 44 students = 1540.

**Step 3 :**

Total weight of 80 students (whole class) is

= 1440 + 1540

= 2980

**Step 4 : **

Find the average weight of the whole class.

Average weight of the whole class is

= Total weight / No. of students

= 2980/80

= 37.25 kg

Hence, the average weight of the whole class is 37.25 kg.

After having gone through the stuff given above, we hope that the students would have understood "Worksheet on average"

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