Question

Two series a and b with equal means have standard deviations 9 and 10 respectively which series is more consistent

Answer 1

Answer:

Ans is A series because coefficient of variation is lesser

Step-by-step explanation:

If the two series have equal means then the series with greater Standard deviation or variance is called more variable or Dispersed than the other.

Also the series with lesser value of standard deviation (or variance ) is said to be more consistent than the other.

Please check the image for complete formula and proof and if it happen opposite way then we have SD same and mean different for that also please check second pic .

Answer 2

Series B is more consistent.

For statistical analysis we use the expressions standard deviation and mean

Mean is the average of all data points

Mean = u = 1/N ( ∈xi)

Standard deviation = σ =√ 1/N ∈ ( xi - u )²

Here it is possible to map the distribution. It's the same mean of two different series, and one's standard deviation is greater than another, which varies in the distribution curve.

The one with small deviation will have a sharp peak and data points are closer to the mean. The one with large deviation will have a spreading peak and data points will be scattered around mean.

Thus,

A has a σ = 9 and B  has σ = 10

Thus, data points of B are more evenly distributed than A

Therefore, series B is more consistent.