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

Answer: (d)

Sum of marks of top 5 students = 40 × 86 – 35 × 85

= 3440 – 2975 = 465

∴ Their average = $465/5$ = 93

Answer: (d)

The sum of 50 observations = 50 × 36 = 1800

The correct mean

= ${1800 - 23 + 48}/50$

= $1825/50$ = 36.5

Aliter : Using Rule 26,

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

Here, n = 50, m = 36

a = 48, b = 23

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

= 36 +${(48 – 23)}/50$

= 36 +$25/50$ = 36.5

Answer: (d)

Difference of numbers = 82 – 28 = 54

∴ Required average = 60 + $54/27$ = 62

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 = 27, m = 60

b = 28, a = 82

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

= 60 +${(82 - 28)}/27$

= 60 +$54/27$ = 62

Answer: (b)

Sum of 9 integers = 9 × 11 = 99.

New average = ${90+ 23- 32}/9$ = $90/9$ =10

Aliter : Using Rule 26,

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

Here, n = 9, m = 11

a = 23, b = 32

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

= 11 +${(23 -32)}/9$

= 11 +${(-9)}/9$

= 11 – 1 = 10

Answer: (c)

Difference of correct and incorrect marks = 64 – 46 = 18

∴ Correct mean = 52 + $18/36$ = 52.5

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 = 36, m = 52

a = 64, b = 46

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

= 52 +${(64 – 46)}/36$

= 52 + $18/36$

= 52 + $1/2$ = 52.5

Answer: (c)

Weight of the new man = 55 +$1/3$ ×12 = 59 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 = 12, T = 55, t = $1/3$

Weight of new man = T + Nt

= 55 + 12 ×$1/3$

= 55 + 4 = 59 kg.