Average Test-4 (Calculating average after replacement of data)

Answer: Option C

Explanation

Given,

The average weight of 10 horseman in a boat is increased by 1.5 kg

= 10×1.5= 15

 when one of the crew, who weighs 68 kg is replaced by a new man

∴ The weight of the new man= (Average weight of 10 horseman +weighs 68 kg is replaced by a new man)

= 15+68= 83 kg

Hence, Option C is correct.

Answer: Option B

Explanation

Given,

The average age of a family 4 members was 24 yrs

= 24×4= 96 yrs

Total age of 4 members, 10 years ago

= [96+(10×4)]

= 136 yrs

Two children are born (4 members +2 child)

= 6×24=144 yrs

Sum of the ages two children

= 144-136= 8

Let the age of younger child be 'x' years

The age of the elder child =(x+2) years 

∴ The present age of the youngest child

= x(x+2)=8

= 2x+2=8

= 2x=6

= x= 3

Hence, Option B is correct.

Answer: Option B

Explanation

Given,

Average of 18 observations is recorded as, 124

⇒18×24= 2232

Later, it was found that two observations with values 64 and 28 were entered wrongly as 46 and 82

Correct total of 18 observations

=2232-(46+82)+(64+28)

=2196

The correct average of the 18 observations=$\frac{2196}{18}=122$

Hence, Option B is correct.

Answer: Option C

Explanation

According to the question

we know the formula,

Mean(Avg)=$\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{Number} \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)}$

Given, Mean (Avg) = 28, N= 10

⇒ $28=\frac{\mathrm{S}}{10}$= 280

Later, it was discovered that one observation 14 was misread as 24

= 24-14= 10

∴ The correct mean is

 $$\begin{gathered} =\frac{\mathrm{S}-10}{\mathrm{N}} \\ =\frac{280-10}{10} \\ =\frac{270}{10}=27 \end{gathered}$$

Hence, Option C is correct.

Answer: Option D

Explanation

According to the question

we know the formula,

Mean(Avg)=$\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{Number} \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)}$

Given, Mean (Avg)= 31, N= 20

 $$\begin{gathered} 31=\frac{\mathrm{S}}{20} \\ \mathrm{S}=20\times 31=620 \end{gathered}$$

But an observation was taken as 52 instead of 27

= 52-25=27

∴ The correct mean of 20 observations is

 $$\begin{gathered} =\frac{\mathrm{S}-27}{\mathrm{N}} \\ =\frac{620-27}{20} \\ =\frac{593}{20}=29.65 \end{gathered}$$

Hence, Option D is correct.