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

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: (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)

Total weight increased = 1 × 25 = 25 kg

∴ Weight of new person = 60 +25 = 85 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 = 25, T = 60 t = 1

Weight of New person = T + Nt

= 60 + 25 × 1 = 85 Kg

Answer: (d)

Total marks obtained by 5 students = 50 × 5 = 250.

Now, in this total marks, 84 is included instead of 48.

∴ Correct total marks = 250 – 84 + 48 = 214

∴ Correct average = $214/5$ = 42.8

Aliter : Using rule 26,

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

Here, n = 5, m = 50

a = 48, b = 84

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

= 50 +${(48-8)}/5$

= 50 - $36/5$

= 50 – 7.2 = 42.8

Answer: (d)

Total length of 20 measurements = 56 × 20 = 1120 cm

Correct length of 20 measurements = 1120 – 64 + 61 = 1117

Correct average = $1117/20$ = 55.85 cm

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 = 56

a = 61, b = 64

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

= 56 +$({61-64}/20)$

= 56 -$3/20$

= 56 – 0.15 = 55.85 cm

Answer: (d)

Correct total of 10 numbers = 15 × 10 – 26 + 36 = 160

∴ Correct average = $160/10$ = 16

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 = 10, m =15

a = 36, b = 26

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

= 15 +${(36 – 26)}/10$

= 15 + 1 = 16