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

Answer: (d)

Difference = 31 – 17 = 14

∴ Required average = 18 +$14/7$ = 20

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 = 7, m = 18

a = 31, b = 17

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

= 18 +${(31 – 17)}/7$

= 18 +$14/7$

= 18 + 2 = 20

Answer: (b)

Difference = 15 + 23 – 51 – 32 = –45

∴ Correct average = 30 -$45/10$ = 25.5

Aliter : Using Rule 27,

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

Here, n = 10, m = 30

a = 15, b = 23

p = 51, q = 32

Correct Average

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

= 30 + ${(15 + 23 - 51 – 32)}/10$

= 30 + $({38-83}/10)$

= 30 - $45/10$

= 30 – 4.5 = 25.5

Answer: (d)

Difference = 97 – 79 = 18

True average = 75 + $18/20$ = 75.9

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 = 75

a = 97, b = 79

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

= 75 +${(97 -79)}/20$

= 75 +$18/20$

= 75 + 0.9 = 75.9

Answer: (b)

Difference = 62 – 26 = 36

∴ Required average = 47 +$36/20$ = 47 + 1.8 = 48.8

Aliter : Using Rule 26,

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

Here, n = 20, m = 47

a = 62, b = 26

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

= 47 + ${(62 – 26)}/20$

= 47+$36/20$

= 47 + 1.8 = 48.8

Answer: (d)

Corrected mean = ${80 × 10 – 60 + 50}/10$

= ${800 – 10}/10$ = $790/10$ = 79

Aliter : Using Rule 26,

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

Here, n = 10, m = 80

a = 50, b = 60

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

= 80+$ {(50- 60)}/10$

= 80 – 1 = 79

Answer: (b)

Difference = 86 – 68 = 18

∴ Actual average = 58 + $18/100$ = 58.18

Aliter : Using Rule 26,

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

Here, n = 100, m = 58

a = 86, b = 68

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

= 58 +${(86 -68)}/100$

= 58 + $18/100$

= 58 + 0.18 = 58.18