Question

. If the standard deviation of the numbers 2, 4, 5 & 6 is a constant a, then find the standard deviation of the numbers 4, 6, 7 & 8.

Select one:

a. 2a

b. A+2. 

c. 4a

d. A​

Answer 1

If the standard deviation of the numbers 2, 4, 5 & 6 is a constant a, then the standard deviation of the numbers 4, 6, 7 & 8 is a

Correct question : If the standard deviation of the numbers 2, 4, 5 & 6 is a constant a, then find the standard deviation of the numbers 4, 6, 7 & 8.

a) a + 2 b) 2a c) 4a d) a

Given :

The standard deviation of the numbers 2, 4, 5 & 6 is a constant a

To find :

The standard deviation of the numbers 4, 6, 7 & 8

a) a + 2

b) 2a

c) 4a

d) a

Solution :

Step 1 of 2 :

Write down the standard deviation of the given data

Here it is given that the standard deviation of the numbers 2, 4, 5 & 6 is a constant a

Step 2 of 2 :

Find standard deviation of the numbers 4, 6, 7 & 8.

4 = 2 + 2

6 = 4 + 2

7 = 5 + 2

8 = 6 + 2

Thus we see that there is a change of origin ( i.e 2 ) from the old data set to new data set

Now we know that standard deviation is independent of the change of origin

Thus the standard deviation of the new set of numbers 4, 6, 7 & 8 will remain the same as of old data set

Therefore the standard deviation of the numbers 4, 6, 7 & 8 is a

Hence the correct option is d) a

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Answer 2

option d is correct, constant a

Given

• standard deviation of the numbers 2, 4, 5 & 6 is a constant a

To find

• the standard deviation of the numbers 4, 6, 7 & 8.

Solution

we are provided with the standard deviation of the numbers 2,4,5 and 6 and I asked to find the standard deviation of numbers 4, 6 ,7 and 8

we know that standard deviation is the measure of dispersion that estimates the extent to which the observation vary from the central value.

standard deviation of numbers 4, 6 ,7 and 8,

the numbers could be a written in the form of,

4 = 2 + 2

6 = 4 + 2

7 = 5 + 2

8 = 6 + 2

we are provided that the standard deviation of 2, 4, 5 and 6 is a .From above, it could be understood that two is being added to each number, indirectly it implies the change of origin.

we know that standard deviation does not change with the change of origin. Therefore, the standard deviation for the given set of numbers would also be the constant a

option d is correct.