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

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)

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: (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.

Answer: (b)

Difference in average = 1.8

∴ Difference between the number and the number formed by interchanging the digits

= 1.8 × 10 = 18

(Since 53 – 35 = 18)

∴ Number = 35

∴ Difference of digits = 5 – 3 = 2

Answer: (d)

Total weight of A, B and C = 84 × 3 = 252 kg.

Again, A + B + C + D = 80 × 4 = 320 kg.

∴ D = (320 – 252) kg. = 68 kg.

E = 68 + 3 = 71 kg.

B + C + D + E = 79 × 4 = 316 kg.

Now, (A + B + C + D) – (B + C + D +E) = (320 – 316) kg.

∴ A – E = 4 kg.

or A = 4 + E = 4 + 71 = 75 kg

Answer: (c)

Weight of the new student

= (40 + 15 × 1.5) kg

= (40 + 22.5) kg

= 62.5 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 = 15, T = 40, t = 1.5

Weight of new Person = T + Nt

= 40 + 15 × 1.5

= 40 + 22.5

= 62.5 kg.