Question

True or False? The first distribution shown below has a smaller standard deviation than does the second distribution. A) 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22. B) 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122

Answer 1

Distribution A:
X m = ( 11 + 12 + 13 + 14 +....+ 22 ) : 12 = 198 : 12 = 16.5
s² ( A ) = ( 5.5² + 4.5² + 3.5² +.....+ 3.5² + 4.5² + 4.5² ) /11
Distribution B :
X m = ( 111 + 112 + 113 + .....+122 ) : 12 = 1398 : 12 = 116.5
s² ( B ) = ( 5.5² + 4.5² + 3.5² + ... + 3.5² + 4.5² + 5.5²) /11
s² ( A ) = s² ( B )
s ( A ) = s ( B ) - standard deviations are the same.
Answer: False.