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

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: (b)

Sum of 50 numbers = 50 × 38 = 1900

Sum of 48 numbers = 1900 – 45 – 55 = 1800

∴ Required average = $1800/48$ = 37.5

Answer: (a)

Correct sum of 9 observations

= 9 × 35 – 18 + 81

= 315 + 63 = 378

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

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

Answer: (b)

Difference = 15 + 23 – 51 – 32 = –45

∴ Correct average = 30 -$45/10$ = 25.5

Aliter : Using Rule 27,

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

Here, n = 10, m = 30

a = 15, b = 23

p = 51, q = 32

Correct Average

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

= 30 + ${(15 + 23 - 51 – 32)}/10$

= 30 + $({38-83}/10)$

= 30 - $45/10$

= 30 – 4.5 = 25.5

Answer: (d)

Difference = 31 – 17 = 14

∴ Required average = 18 +$14/7$ = 20

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 = 7, m = 18

a = 31, b = 17

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

= 18 +${(31 – 17)}/7$

= 18 +$14/7$

= 18 + 2 = 20