Average Test-7 (Complete Revision)

Answer: Option A

Explanation

Given set of scores= 253, 124, 255, 534, 375, 101, 443, 76

We know the formula,

 $\mathrm{Average} \left(\mathrm{A}\right)=\frac{\mathrm{Sum} \mathrm{of} \mathrm{given} \mathrm{values} \left(\mathrm{S}\right)}{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{values} \left(\mathrm{N}\right)}$

 Here,

 Sum of given values(S)

=12.5+11.6+13.2+15.6+9.8

= 62.7

Total number of values(N)= 5

Substituting these values we get (A),

 $= \frac{62.7}{5}=12.54$

Hence, Option A is correct.

Answer: Option D

Explanation

Even number between 11 to 63 = 12, 14, 16, .......60, 62.

This is a series of consecutive even numbers

According to the formula,

The average of consecutive numbers=$\frac{\mathrm{First} \mathrm{number}+\mathrm{Last} \mathrm{number}}{2}$

$$\begin{gathered} =\frac{12+62}{2} \\ =\frac{74}{2} \\ =37 \end{gathered}$$

Hence, Option D is correct.

Answer: Option E

Explanation

According to the question

We know the formula,

Mean=$\frac{\mathrm{sum} \mathrm{of} \mathrm{observation}}{\mathrm{Number} \mathrm{of} \mathrm{observation}}$

Sum of observation =70

Number of observation=20

∴ Mean=$\frac{70}{20}=3.5$

Here observation starts from 23 

∴ Mean =23+3.5=26.5

Hence, Option E is correct.

Answer: Option B

Explanation

Let the eight sequentially number are = x+x+1+x+2+x+3+x+4+x+5+x+6+x+7

= 8x+28

According to the question

$$\begin{gathered} =\frac{\mathrm{x}+3+\mathrm{x}+4}{2}=6 \\ =\frac{2\mathrm{x}+7}{2}=6 \end{gathered}$$

= 2x+7=12

= 2x =5

x=$\frac{5}{2}$

Sum of all eight numbers= 8x+28

     = 8$\left(\frac{5}{2}\right)$+28

     = 20+28= 48

Hence, Option B is correct.

Answer: Option B

Explanation

According to the question

We know the formula,

Average of the cube's 1st 'n' natural numbers= $\frac{\mathrm{n}(\mathrm{n}+1{)}^2}{4}$

where, n=5

∴ Required average =$\frac{5{\left(5+1\right)}^2}{4}=\frac{5\times 36}{4}$

= 5×9= 45

Hence, Option B is correct.