model 5 find new average from error Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Correct sum of 9 observations

= 9 × 35 – 18 + 81

= 315 + 63 = 378

∴ Required correct average = $378/9$ = 42

Answer: (a)

Difference of two observations = 73 – 48 = 25

∴ New average = 13 + $25/25$=14

Aliter : Using Rule 26,

If average of n numbers is m later on it was found that a number 'a’ was misread as 'b’.

The correct average will be = m +${\text"(a-b)"}/ \text"n"$.

Here, n = 25, m = 13

a = 73, b = 48

Correct Average = m + ${\text"(a-b)"}/ \text"n"n$

= 13 +${(73- 48)}/25$

= 13 + 1 = 14

Answer: (b)

Let the number of candidates be x, then

60x – 45x = 30 × 100

⇒ 15x = 3000

⇒ x = 200

Answer: (d)

Required answer = 30 + 20 × 0.75

= 30 kg + 15 kg = 45 kg

Aliter : Using Rule 18,

If in the group of N persons, a new person comes at the place of a person of 'T’ years, so that average age,

increases by 't’ years

Then, the age of the new person = T + N.t.

Here, N = 20, T = 30, t = 0.75

Weight of New student = T + Nt

= 30 + 20 × 0.75

= 30 + 15 = 45 kg

Answer: (d)

Total weight increased =$1/2$ × 50 = 25 kg.

∴ Weight of the new man = 50 + 25 = 75 kg.

Aliter : Using Rule 18,The age of the new person = T + N.t.

Here, N = 50, T = 50, t = $1/2$

Weight of New boy = T + Nt

= 50 + 50 × $1/2$ = 75 kg.

Answer: (d)

Difference = 97 – 79 = 18

True average = 75 + $18/20$ = 75.9

Aliter : Using Rule 26,

If average of n numbers is m later on it was found that a number 'a’ was misread as 'b’.

The correct average will be = m +${\text"(a-b)"}/ \text"n"$.

Here, n = 20, m = 75

a = 97, b = 79

Correct mean = m + ${\text"(a - b)"}/\text"n"$

= 75 +${(97 -79)}/20$

= 75 +$18/20$

= 75 + 0.9 = 75.9