Question

if the standard deviation of a data is 4.5 and if each value of the data is decreased by 5 then find the new standard deviation​

Answer 1

Answer:

The new standard deviation = 4.5

Step-by-step explanation:

As per the given question,

We have been provided the standard deviation of a data = 4.5

As we know that the formula of standard deviation is

$Standard \ deviation \ = \sqrt{\frac{\sum_{1}^{n}(x_{i}-\bar x)}{(n-1)}}$,

x-bar = mean of the data

As per question if each data is decreased by 5, that means. mean value of the data will be changed but in overall standard deviation, there will be no change.

That means the new standard deviation is same as the old standard deviation.

Hence, the required standard deviation = 4.5

Answer 2

Answer:

4.5

Step-by-step explanation:

Since, the standard deviation of a data is 4.5

The formula for the standard deviation is given as:

$s.d = \sqrt{\frac{ ∑ (x-x1)^{2} }{n} }$

where x is the data given;

x1 is the mean;

and n is the no. of data given

So , $4.5 = \sqrt{\frac{ ∑ (x-x1)^{2} }{n} }$

Now, we have to make the changes to the given expression, as we have to decrease the value of the data by 5 units.

So, if we decrease the data , accordingly the value we will get is;

$s.d = \sqrt{\frac{ ∑ ((x-5)-(x1-5))^{2} }{n} }$

which will comes out to be;

$s.d = \sqrt{\frac{ ∑ ((x-x1)^{2} }{n} }$

So, the value comes out to be as it is in the above, without changing it.

So, the standard deviation will not change at all , after decreasing the data by 5.

So, the new standard deviation will be 4.5