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

Answer: Option A

Explanation

According to the question

We use the formula,

Value of new observations= a - nb 

[here '-' sign (a-nb) has been taken as average decreases in this case]

Here, n=30, a=25 yr, b= $\frac{3}{12}$ yr

Age of keerthi = a - nb

= 25-30×$\frac{3}{12}$

= 25-$\frac{15}{12}$

= 25-7.5= 17.5 yr

Hence, Option A is correct.

Answer: Option C

Explanation

According to the question

We use the formula,

Value of new observations= a + nb

Here, n=10, a= 42+38= 80 kg, b= 1 kg

Total weight of both men = a+nb

= 80+10×1

= 90 kg

Average wieght of both men= $\frac{90}{2}$=45 kg

Hence, Option C is correct.

Answer: Option B

Explanation

According to the question

We use the formula,

Value of new observations= a + nb

[Average increases, hence '+' sign (a+nb) has been taken.]

Here, n=11, a= 32+33+34= 99 yr, b= 2 yr

Age of three women = a+nb

= 99+11×2

= 99+22= 121 yr

Average age of three women

=$\frac{121}{3}$= 40.33 kg (or) = $40\frac{1}{3}$ yr

Hence, Option B is correct.

Answer: Option D

Explanation

According to the question

We use the formula,

Value of new observations= a - nb

[here, Average decreases, hence '-' sign (a-nb) has been taken.]

Here, n=24, a= 12+13+14=39 yr, b= 2 months= $\frac{2}{12}$ yr

Total age of 3 males = a-nb

= 39-24×$\frac{2}{12}$ 

= 39-4= 35 yr

Average age of 3 males= $\frac{35}{3}= 11\frac{2}{3}$ yr

Hence, Option D is correct.

Answer: Option A

Explanation

According to the question

Total correct weight = 40×60-36+33

= 2400 - 3

= 2397 kg

The actual average weight of the students in the class

$= \frac{2397}{60}$

= 39.95 kg

Hence, Option A is correct.