Question

Susan keeps track of the number of tickets sold for each play presented at The Community Theater. Within how many standard deviations from the mean do all the values fall? 135, 71, 69, 80, 158, 152, 161, 96, 122, 118, 87, 85

Answer 1

The Mean = (135 + 71 + 69 + 80 + 158 + 152 + 161 + 96 + 122 + 118 + 87 + 85 ) : 12 = 111.166

The smallest value : 69

The greatest value : 161

s² = ∑( x i - x )² / ( n - 1 )

s² = ( 568.274 + 1613.3 + 1777.97 + 971.32 + 2193.42 + 1667.4 + +2483.42 + 230 + 117.38 + 46.7 + 584 + 684.66 )  : 11

s² = 1176.1676

s = √s² = √1176.1676

s ( Standard deviation ) = 34.295

All the values fall within 2 standard deviations:

 x (Mean) - 2 s and  x + 2 s