I have two cases: 1. If I add a constant to them, does the mean, standard deviation and z score change? What I think: Mean changes, std deviation doesn't change and z score doesn't change. 2. If I blackuce all the numbers by 5% does the mean, standard deviation and z score change? What I think: Mean changes by 5%, standard deviation changes but the percentage difference remains the same, and the z score changes by 2.5% Am I thinking correctly?

assuolareuz

assuolareuz

Open question

2022-08-17

I have two cases:
1. If I add a constant to them, does the mean, standard deviation and z score change?
What I think: Mean changes, std deviation doesn't change and z score doesn't change.
2. If I blackuce all the numbers by 5% does the mean, standard deviation and z score change?
What I think: Mean changes by 5%, standard deviation changes but the percentage difference remains the same, and the z score changes by 2.5%
Am I thinking correctly?

Answer & Explanation

kilinumad

kilinumad

Beginner2022-08-18Added 21 answers

Suppose that you have x 1 , x 2 , , x n . Using the definitions of those statistics, you have
x ¯ = x i n
s = ( x i x ¯ ) 2 n 1
z s c o r e o f x i = x i x ¯ s
Now if you add a constant to all observations, it is easy to see that x ¯ changes by the same amount, but the other two statistics remain the same.
If you blackuce all numbers by 5%, each x i becomes 0.95 x i . Thus, both x¯ and s decrease by 5% as well, but the z-score remains the same.

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