Answer to Question #349515 in Statistics and Probability for Ashii

Question

(a) The mean and standard deviation of a set of values are 25 and 5, respectively. If a constant value 5 is added to each value, the coefficient of variation of the new set of values is equal to 10%.

(b) If (A) = 90, (AB) = 40, N = 150 and (β) = 80 then (αβ) = 30.

Answer 1

(a)

The mean and standard deviation of a set of values are 25 and 5, respectively.

Adding a constant $c$ to each value mean will be changed by adding a constant $c$ and standard deviation remain the same.

Then $\mu_{new}=20+5=25, \sigma_{new}=5.$

$$coefficient\ of\ variation=\dfrac{\sigma_{new}}{\mu_{new}}\cdot100\%$$

$$=\dfrac{5}{25}\cdot100\%=20\%\not=10\%$$

The statement that the coefficient of variation of the new set of values is equal to 10% is False.

(b)

In a 2 × 2 contingency table of two attributes :

$$\def\arraystretch{1.5} \begin{array}{c:c:c:c} A\darr\setminus B\to & B & \beta & Total \\ \hline A & (AB)=40 & (A\beta)=50 & 90 \\ \hdashline \alpha & (\alpha B)=30 & (\alpha \beta)=30 & 60 \\ \hdashline Total & (B)=70 & (\beta)=80 & 150 & \\ \hdashline \end{array}$$