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

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

Answer: (c)

Weight of the new oarsman = 60 + 8 × $3/2$

= 60 + 12 = 72 kg

Aliter : Using Rule 18,

Here, N = 8, T = 60, t = $3/2$

Weight of new man = T + Nt

= 60 + 8 × $3/2$

= 60 + 12 = 72

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)

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

= 3440 – 2975 = 465

∴ Their average = $465/5$ = 93

Answer: (c)

Total weight increased = 1 × 25 = 25 kg

∴ Weight of new person = 60 +25 = 85 kg

Aliter : Using Rule 18,

If in the group of N persons, a new person comes at the place of a person of 'T’ years, so that average age,

increases by 't’ years

Then, the age of the new person = T + N.t.

Here, N = 25, T = 60 t = 1

Weight of New person = T + Nt

= 60 + 25 × 1 = 85 Kg