Statistics as level cie question help please

ii) (ii) new mean = 896/17 (= 52.7)
712 + 22^2 /17- 24 + (72 − 50) ^2/17
new sd = 7.94

*i do NOT GET why u have to subtract 50 from 72 and can just someone explain the steps for me please , I need help

I think it's just because you're finding the new Var(x), after the new score of 72 has been included, by calculating the new Var(x-50).

Var(x) = Var(x - 50) = Σ((x - 50)^2)/n - ((Σ(x - 50))/n)^2

I think it's just because you're finding the new Var(x), after the new score of 72 has been included, by calculating the new Var(x-50).

Var(x) = Var(x - 50) = Σ((x - 50)^2)/n - ((Σ(x - 50))/n)^2

Yes I do know that , but my question is Why is 72 subtracted from 50 , what is the reason , why is it like that ,

The usual reason for processing linearly shifted data rather than raw data is to reduce the size of the numbers involved in computation - especially the squared numbers. However, in this case the numbers are not huge so I suspect the question is just designed to check students' ability to cope with linearly shifted data (or coded data as it's often called).

Why did we subtract 50 from 72? The rule doesn’t say that

Well you have to add the 72 into sigma (x-50) where 824>896 and 16 >17.

You then calculate the other parts of the SD formula.

You need to post what you have tried otherwise your post looks like "do my homework".

No need to have 3 different threads on the same question.

I’ve merged them all.

No need to have 3 different threads on the same question.

I’ve merged them all.

So do u know how to solve that ?

old_engineer has already explained it

He hasn’t answered my question ? Why do we subtract 72 from 50 ?

Yes he did but you just seem as if you’re unhappy with his answer...

Every value in the data set has 50 subtracted from them, so you need to subtract 50 from your new piece of data if you are to incorporate it into the rest.
As for why we choose 50, you’d need to ask the actual person who came up with this question because it could’ve been any other number and there’s no actual need for it!

I do know the answer and steps for part 1 , I have a problem in part 2 .

Esme noted the test marks, x, of 16 people in a class. She found that Σ x = 824 and that the standard
deviation of x was 6.5.
(i) CalculateΣ(x−50)andΣ(x−50)2. [3]
(ii) One person did the test later and her mark was 72. Calculate the new mean and standard deviation of the marks of all 17 people. [3]


(i) Σ(x – 50) = 824 – 16 × 50 = 24
Σ(x − 50)^2 =712

ii) (ii) new mean = 896/17 (= 52.7)
712 + 22^2 /17- 24 + (72 − 50) ^2/17
new sd = 7.94


*i do NOT GET why u have to subtract 50 from 72 and can just someone explain the steps for me please , I need help