Data A has a mean of 100 and standard deviation of 10 - Data B has a mean of 1000 and standard deviation of 50 - Which data shows more variability-A- Data B shows more variabilityB- Both show equal variabilityC- Data A shows more variabilityD- Nothing can be concluded

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Absolute and Relative Measures of Dispersion

Data A has a ...

Question

Data A has a mean of 100 and standard deviation of 10. Data B has a mean of 1000 and standard deviation of 50. Which data shows more variability?

Data A shows more variability

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Data B shows more variability

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Both show equal variability

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Nothing can be concluded

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Solution

The correct option is A Data A shows more variability
To compare dissimilar data, relative measures should be used. Here, the coefficient of variation of set A and set B can be compared.

$C O V_{A} = \frac{10}{100} \times 100 = 10 %$
$C O V_{B} = \frac{50}{1000} \times 100 = 5 %$

Hence, data A shows more variability.

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Data A has a mean of 100 and standard deviation of 10. Data B has a mean of 1000 and standard deviation of 50. Which data shows more variability?

The correct option is A Data A shows more variabilityTo compare dissimilar data, relative measures should be used. Here, the coefficient of variation of set A and set B can be compared. COVA=10100×100=10% COVB=501000×100=5% Hence, data A shows more variability.