Question

if the mean of Aand B Siries are 15 and 20. Variance of A and B series are 25 and 16, which of the two series are more consistant:
Select one
a Nether Anor B consistant
b. Series A and B both are equally consistant
c. Senes A
od Series В​

Answer 1

Answer:

B

Step-by-step explanation:

B.series A and V both are equally consistant

Answer 2

Series B is more consistent than series A. (option d)

Given,

For series A:

mean = 15, variance = 25, and

For series B:

mean = 20, variance = 16.

To find,

Which series, A or B, is more consistent.

Solution,

The mean ($\mu$) and variance ($\sigma^2$) of two series A and B are given here, which are as follows.

For series A,

$\mu_A =15,\\\sigma_A^2=25 \implies \sigma_A = 5,$

For series B,

$\mu_B =20,\\ \sigma_B^2=16 \implies \sigma_B = 4.$

$\sigma$ is the standard deviation.

We have to determine which series is more consistent between A and B.

To find this, we need to find the Coefficient of Variation (CV) of both A and B. The series having lower CV will be more consistent than the one with higher CV.

CV is given as,

$CV=\frac{\sigma}{\mu} \times 100 \hfill ...(1)$

where,

$\sigma$ = Standard deviation, and,

$\mu$ = mean.

Now, CV for series A,

$CV_A=\frac{\sigma_A}{\mu_A} \times 100$

$\implies CV_A=\frac{5}{15} \times 100=\frac{100}{3}$

$\implies CV_A=33.33$

CV for series B,

$CV_B=\frac{\sigma_B}{\mu_B} \times 100$

$\implies CV_B=\frac{4}{20} \times 100=\frac{100}{5}$

$\implies CV_B=20$

Comparing the value of $CV_A$ with that of $CV_B$, we can see that,

$CV_B < CV_A$

Therefore, series B is more consistent than series A. (option d)

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