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

Answer: Option B

Explanation

According to the question

Sum of added quantities - Sum of removed quantities= ±Nx

⇒ (72+61)-(48+65)= ± 20×x

⇒ 133-113= 20×x

⇒ x=$\frac{20}{20}$=1

∴ The actual average = 68+1 =69

Hence, Option B is correct.

Answer: Option A

Explanation

According to the question

Sum of added quantities - Sum of removed quantities= ±Nx

⇒ 25-45= -75×x

⇒ x=$\frac{20}{75}$=0.26

∴ New average = 47-0.26 = 46.73 kg

Hence, Option A is correct.

Answer: Option B

Explanation

According to the question

If the average is increased by 3kg, then the sum of wieght increases by

= 3×4=12 kg

If wieghs 120 kg is replaced by another man 

∴ The weight of the new man

= 120+12=132 kg.

 Hence, Option B is correct.

Answer: Option C

Explanation

According to the question 

Age of new person = Age of removed person-No. of persons × Decrease in average age 

$$\begin{gathered} = 18-20\times \frac{2}{12} \\ =18-\frac{10}{3} \\ =\frac{44}{3} \end{gathered}$$

 = 14.66 (or) =$14\frac{2}{3}$

Hence, Option C is correct.

Answer: Option C

Explanation

According to the question

We use the formula,

Value of new observations= a + nb 

[here '+' sign (a+nb) has been taken as average increases.]

Here, n=6, a=100 kg, b= 3 kg

Weight of new person = a+nb

= 100+6×3

= 100+18

= 118 kg

Hence, Option C is correct.