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

Question

Essence Irwin

Mathematics

12 January, 13:14

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

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Lillianna Howell · 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.