model 5 find new average from error Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

Sum of marks of top 5 students = 40 × 86 – 35 × 85

= 3440 – 2975 = 465

∴ Their average = $465/5$ = 93

Answer: (d)

The sum of 50 observations = 50 × 36 = 1800

The correct mean

= ${1800 - 23 + 48}/50$

= $1825/50$ = 36.5

Aliter : Using Rule 26,

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

Here, n = 50, m = 36

a = 48, b = 23

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

= 36 +${(48 – 23)}/50$

= 36 +$25/50$ = 36.5

Answer: (d)

Difference of numbers = 82 – 28 = 54

∴ Required average = 60 + $54/27$ = 62

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 = 27, m = 60

b = 28, a = 82

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

= 60 +${(82 - 28)}/27$

= 60 +$54/27$ = 62

Answer: (d)

Sum of 18 items

= 55 × 20 – 45 – 30

= 1100 – 75 = 1025

∴ Required average = $1025/18$ = 56.9

Answer: (b)

Correct average = 35 - $({61 - 16}/20)$

= 35 – $45/20$

= 35 – 2.25 = 32.75

Aliter : Using Rule 26,

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

Here, n = 20, m = 35

a = 16, b = 61

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

= 35 +${(16 - 61)}/20$

= 35 - $45/20$

= 35 – 2.25 = 32.75