Statistics Question - Find Standard Deviation of 5 numbers but only 4 given.

[JiHbE]

For a sample of size 5, if x1 - x̄ = -5, x2 - x̄ = 9, x3 - x̄ = -7, and x4 - x̄ = -2, then the sample standard deviation is:
Choose one answer.
a. 5.639
b. 6.782
c. None of the other answers are correct
d. 6.305
e. 6.066

Please note that x̄ is x-bar (mean of sample).


This question has been puzzling me. At first I thought there was an error because only 4 numbers are listed but it says there sample size is 5. But, this is a valid question.

So, I'm going to need the x5- x̄ value in order to calculate the standard deviation.
This is where I'm lost... could someone please provide some assistance?

Thank you so much for your time.

 

[mfb]

Can you express the mean in terms of x1 to x5? Rewriting that equation a bit will give you x5 - xmean.

 

[SammyS]

For a sample of size 5, if x1 - x̄ = -5, x2 - x̄ = 9, x3 - x̄ = -7, and x4 - x̄ = -2, then the sample standard deviation is:
Choose one answer.
a. 5.639
b. 6.782
c. None of the other answers are correct
d. 6.305
e. 6.066

Please note that x̄ is x-bar (mean of sample).

This question has been puzzling me. At first I thought there was an error because only 4 numbers are listed but it says there sample size is 5. But, this is a valid question.

So, I'm going to need the x5- x̄ value in order to calculate the standard deviation.
This is where I'm lost... could someone please provide some assistance?

Thank you so much for your time.

Hello JiHbE. Welcome to PF !

What is $\ \ x_1+x_2+x_3+x_4+x_5-5\cdot\bar{x}\ ?$

 

[JiHbE]

Can you tell me how you typed x-bar? :)

What I do know is that:

mean = (x1 + x2 + x3+ x4 + x5)/5

Therefore,

5mean = (x1 + x2 + x3 + x4 + x5)

 

[mfb]

Can you tell me how you typed x-bar? :)

You can see the code via the "quote" button in his post.

Therefore,

5mean = (x1 + x2 + x3 + x4 + x5)

Right. Now you can use your knowledge about $x_1-\bar{x}$ and so on.