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​Consider the following two data sets:​whereare independent random variables and is a positive constant. The ratio of the standard deviation and
Question

​Consider the following two data sets:

​where

are independent random variables and 

is a positive constant. The ratio of the standard deviation and the average values for the data sets,

are related by

A.

B.

C.

D.

Correct option is A

An average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean – the sum of the numbers divided by how many numbers are in the list. For example, the mean average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5.

In statistics , the standard deviation is a measure of the amount of variation of the values of a variable about its mean. A low standard deviation indicates that the values tend to be close to the mean(also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation. The standard deviation of a random variablesamplestatistical population ,data set, or probability distribution is the square root of its variance. (For a finite population, variance is the average of the squared deviations from the mean.)

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