model 4 find nth average from 1st & last number Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Using Rule 1,

x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 = 6.5 × 8 = 52

⇒ 8x + 28 = 52

⇒ 8x = 52 – 28 = 24

⇒ x = 3

∴ Required average =${3+10}/2$= 6.5

Answer: (b)

When each number is multiplied by 8, the new average gets multiplied by 8.

i.e., 21 × 8 = 168

Answer: (c)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

According to question,

The average of 9 numbers = 30

Now,The total of 9 numbers

= 30 × 9 = 270

The average of first 5 numbers = 25

∴ The total of first 5 numbers = 25 × 5 = 125

and Total of last 3 numbers = 3 × 35 = 105

Hence, required answer

= 270 – (125 + 105)

= 270 – 230 = 40

Answer: (c)

Using Rule 1,

The middle number

= 8 × 6.5 + 8 × 9.5 – 15 × 7

= 52 + 76 – 105

= 128 – 105 = 23

Answer: (b)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Last number

= 30 × 12 – 20 × 11 – 9 × 10

= 360 – 220 – 90

= 360 – 310 = 50