Mean and standard deviation

**ibaraku** · September 3rd 2008, 11:41 AM

Hello guys, I am really confused with this problem:

A list of 10 numbers has a mean of 20, a median of 18, and a standard deviation of 5. The largest number on the list is 39.27. By accident, this number is changed to 392.7
a.What is the value of the mean after the change?
b.What is the value of the standard deviation after the change?

I just need a push in the right direction
thanks

**mr fantastic** · September 3rd 2008, 05:37 PM

Originally Posted by ibaraku

Hello guys, I am really confused with this problem:

A list of 10 numbers has a mean of 20, a median of 18, and a standard deviation of 5. The largest number on the list is 39.27. By accident, this number is changed to 392.7
a.What is the value of the mean after the change?
b.What is the value of the standard deviation after the change?

I just need a push in the right direction
thanks

a. $\bar{x} = 20 = \frac{\sum_{i=1}^{10} x_i}{10} \Rightarrow \sum_{i=1}^{10} x_i = 200$ .

After the mistake: $\sum_{i=1}^{10} x_i = 200 - 39.27 + 392.7 = \, ......$

Therefore $\bar{x} = \, ....$

A similar idea can be used to solve b.

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