Variance And Standard Deviation

Given:

and mean( )

Then as there are 8 observations , so

Therefore, the two terms are respectively.

Now, Then Variance( )

Given:

• Dataset 1: Coefficient of variation (CV) = 50, Variance = 25
• Dataset 2: Coefficient of variation (CV) = 75, Variance = 36
• Let and be the sample means

Step 1: Recall the formula for coefficient of variation: where is the standard deviation.

Step 2: For Dataset 1:

Step 3: For Dataset 2:

Step 4: Calculate the sum of means:

The value of is 18.

Given:

• Four observations:
• Sum of squares:
• Sum of observations:

We need to find the variance of these observations.

Step 1: Recall the variance formula for a population:

Step 2: Plug in the given values (n=4):

Given two sets of observations with their means:

First set: 1, 3, 5, a, 9 with mean

Second set: 2, 4, b, 6, 8 with mean

Given that and , we need to find .

Step 1: Calculate the means:

Step 2: Set the means equal:

Step 3: Calculate :

The correct answer is (E) 4.

Let the standard deviation of and be 9.

This means the variance of and is .

Let and be the transformed variables:

The variance of a linear transformation is . Therefore:

The variance of and is 729.