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

Answer: (b)

Difference of numbers = 64 – 46 = 18

Correct average = 50 – $18/10$ = 50 – 1.8 = 48.2

Aliter : Using Rule 26,

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

Here, n = 10, m = 50

a = 46, b = 64

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

= 50 + ${(46 – 64)}/10$

= 50 -$18/10$

= 50 – 1.8 = 48.2

Answer: (d)

Correct sum of 100 items

= 30 × 100 – 32 – 12 + 23 + 11

= 3000 – 44 + 34 = 2990

∴ Required average = 2990 100 = 29.9

Answer: (d)

Required average

= 30+${(28+31-82-13)}/50$

= 30 $(-36/50)$

= 30 – 0.72 = 29.28

Aliter : Using Rule 27,

If the average of n numbers is m later on it was found that two numbers a and b misread as p and q.

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

Here, n = 50, m = 30

a = 28, b = 31

p = 82, q = 13

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

= 30 +${(28+31-82-13)}/50$

= 30 +$({59-95}/50)$

= 30 -$36/50$

= 30 – 0.72 = 29.28

Answer: (d)

According to question,

Total marks = 71 × 14 = 994

Correct total marks

= 994 + (56 – 42) + (32 – 74)

= 994 + 14 – 42 = 966

∴ Required average = $966/14$ = 69

Aliter : Using Rule 27,

If the average of n numbers is m later on it was found that two numbers a and b misread as p and q.

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

Here n = 14, m = 71

a = 56, b = 42

p = 32, q = 74

Correct Average

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

= 71 +${(56+ 32- 42- 74)}/14$

= 71 -$28/14$

= 71 – 2 = 69