Question

PLEASE HELP!!!!!!!!! (Medal will go to best answer.)

Use the standard deviation to identify any outliers in the given data set: {3,4,5,6,8,9,10,30}

Please explain why there is or isn't an outlier and how you'd determine if there is one or not.

Thank you! =)

Answer 1

By the way - the variance is: 66.035

Answer 2

First, find the standard deviation of the data set. To do this, find the mean, then find the distance each point is from the mean, square and sum those distances, and square root the total. Once you have that, check how many standard deviations the data points are from the mean. There's no set definition for what makes a point an outlier; your class may have specified a number of standard deviations that qualifies. Inevitably, with this data set, the answer will be that 30 is an outlier, but you'll need to show why.

Edit: Since you have the variance, you can just take the square root of the variance to find the standard deviation.

Answer 3

Wow! Thanks so much. I found that the variance is: 8.13 - my class didn't specify if this would classify it as an outlier. What do you think?

Answer 4

*sorry I meant that 8.13 is the Standard Deviation

Answer 5

BTW - the mean of the original data set was: 9.375

Answer 6

Well, since you know the standard deviation, and you know the mean, you can find how many standard deviations away from the mean each point is. At some cutoff, you'll say that a point is an outlier if it's more than a certain number of standard deviations away from the mean. With this data set, 30 is more than 2 standard deviations away from the mean, so it's definitely an outlier.

Answer 7

Okay, perfect! Thank you so much! I really appreciate your thoroughness! If I could give you another medal, I would. :)