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

Question : 1 [SSC CGL Tier-II 2014]

The average of six numbers is 20. If one number is removed, the average becomes 15. What is the number removed ?

a) 35

b) 5

c) 45

d) 112

Answer: (c)

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

= 6 × 20 – 15 × 5

= 120 – 75 = 45

Question : 2 [SSC CHSL 2011]

A tabulator while calculating the average marks of 100 students of an examination, by mistake enters 68, instead of 86 and obtained the average as 58; the actual average marks of those students is

a) 57.82

b) 58.18

c) 57.28

d) 58.81

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

Question : 3 [SSC Multi-Tasking Staff 2013]

The average of l0 items was found to be 80 but while calculating, one of the items was counted as 60 instead of 50. Then the correct average would have been :

a) 79.25

b) 69

c) 79.5

d) 79

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

Question : 4

The mean of 20 items is 47. Later it is found that the item 62 is wrongly written as 26. Find the correct mean.

a) 47·7

b) 48·8

c) 46·6

d) 49·9

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

Question : 5

The average of 18 observations is recorded as 124. Later it was found that two observations with values 64 and 28 were entered wrongly as 46 and 82. Find the correct average of the 18 observations.

a) 122

b) 111$7/9$

c) 137$3/9$

d) 123

Answer: (a)

Difference in observations

= 64 + 28 – 46 – 82 = – 36

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

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