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Find a data set (10 numbers between 1-50) where fewer than half of the numbers fall within...?
...one standard deviation of the mean?
This is one problem of a stat worksheet and I haven't figured how to solve it. I even resorted to guessing and checking and even that wasn't leading me into any direction. So I was hoping for help. How best to approach this problem and such, please not just the answer. Thank you so much!
I'm not getting that that data set works. :/ And actually, let me edit this, it can actually be 0-50
1 Answer
- FlashRubinoLv 68 years agoFavorite Answer
I fooled around with this a little, and finally realized that the key is to minimize the deviation for the 4 allowable data points within plus/minus 1 sd. Set 4 points equal to the mean, then set three points at mean-x and 3 ponts at mean+x.
As an illustration, choose 24,24,24,25,25,25,25,26,26,26.
By inspection we can see that the sd will be less than 1, so the ONLY data points in the interval are at the mean. (This also works with 1,1,1,25,25,25,25,50,50,50, so I don't see why it wouldn't always work.
Just knock your sd way down by having 4 values with 0 deviaition, then balance the rest so the mean comes out in the right place.