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

Answer: (a)

Correct sum of marks obtained by the student

= 88 × 6 – 86 + 68

= 528 – 86 + 68 = 510

∴ Correct average = $510/6$ = 85

Aliter : Using Rule 26,

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

Here, n = 6, m = 88

a = 68, b = 86

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

= 88 +${(68 - 86)}/6$

= 88 - $18/6$ = 85

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)

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

Answer: (a)

Required Average

= ${100 × 46 – 61 – 34 + 16 + 43}/90$

= ${4600 – 36}/90$ = $4564/90$ = 50.7