Question

Attachment in pic

Answer 1

I can't remember how to do this please @ganeshie8

Answer 2

@thomaster

Answer 3

mean:
\[\bar{x}=\frac{1}{n}\sum_{i=1}^n x_i\]

Here, \(x_i\) are your data points. So, \(x_1=8, x_2=1, x_3=5, x_4=1, x_5=5\), and \(n\) is the number of data points you hate (there are only 5 here).
So basically you just do: \[ \bar{x}=\frac{8+1+5+1+5}{5}\]

Standard deviation:
\[ s=\sqrt{\frac{1}{n-1}\sum_{i=1}^n({x_i-\bar{x}})^2}\]. You have to subtract each data point with the mean, then square this result, and then add up all of those results together. The you just multiply that result by \(1/(n-1)\) and finally you square root everything!
This would translate as:
\[ s=\sqrt{\frac{1}{5-1}\left[(8-5)^2+(1-5)^2+(5-5)^2+(1-5)^2+(5-5)^2\right]}\]

Answer 4

In b) you essentially do the same, but you just replace the "8" with the value "18" instead.

In c) Since you are replacing the 8 with 18, and 18 is quite larger than the other numbers (1 and 5), they want you to describe how the mean and standard deviation changed from a) to b) (did you notice that the mean increased or decreased? How about the standard deviation?)

Answer 5

That is what they mean by an "extreme score". The 18 is much larger than 1 or 5, so it is considered "extreme".