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The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

$$\begin{array}{|c|c|c|} \hline \textbf{Batsman} & \textbf{Average} & \textbf{Standard deviation} \\\hline \text{K} & \text{31.2} &\text{5.21} \\\hline \text{L} & \text{46.0} &\text{6.35} \\\hline \text{M} & \text{54.4} &\text{6.22} \\\hline \text{N} & \text{17.9} &\text{5.90} \\\hline \end{array}$$

1. $K$
2. $L$
3. $M$
4. $N$

Average only gives the mean value, Standard Deviation gives how close to mean value (consistency) of a sample population distribution.

A standard deviation close to 0 means very close to mean value of a distribution.

Here K has the lowest SD (5.21)
by

Most consistent is the least dispersion in the scores. We have a parameter called Coefficient of Variance which is used to measure relative measure of dispersion between two sets.

Coefficient of Variance(CV) = $\frac{Standard Deviation}{Mean}$

Calculating it for all the four players.

K's CV = 0.167

L's CV = 0.138

M's CV = 0.114

N's CV = 0.329

Larger the value of CV, less consistent the player is.

So the most consistent player is M here

Option C

### 1 comment

And what does standard deviation signify? And why is it's significance given less importance than CoV?

consistent batsman means indirectly asking for lesser coefficient of variance.

coefficient of variance (CV) =standard deaviation/mean

K's CV=0.16

L's CV=0.13

M's CV=0.11

N's CV=0.32

so ans should be C..

### 1 comment

Ans is A, as it is only considered with the rate of variation of score and lesser the variation the more consistent the player is, and Standard deviation is sufficient alone for checking the condition..

See the official ans key of GATE, there also they have given A.

Ans is A, as the question is only concerned with the rate of variation of score and lesser the variation the more consistent the player is, and Standard deviation is sufficient alone for checking the condition..

See the official ans key of GATE, there also they have given A.

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