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

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: (a)

Difference in observations

= 64 + 28 – 46 – 82 = – 36

∴ Correct average = 124 -$36/18$ = 122

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 = 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

Answer: (c)

Required number = sum of six numbers – sum of five numbers

= 6 × 20 – 15 × 5

= 120 – 75 = 45