Question

22 which of the dot plots shows a symmetric distribution? a 9 10 11 12 13 14 15 16 17 18 19 20 b 1 2 3 4 5 6 7 8 9 10 11 12 c 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 d 9 10 11 12 13 14 15 16 17 18 19 20

Explanation:

Step1: Recall the definition of symmetric distribution

A symmetric distribution has a mirror - image appearance about a central value. That is, if we fold the dot - plot along a vertical line through the center, the two halves match exactly.

Step2: Analyze option A

For option A, if we consider the value \(x = 14\) as the potential center. The number of dots on the left - hand side of \(x = 14\) (for values \(10,11,12,13\)) and the number of dots on the right - hand side of \(x = 14\) (for values \(15,16,17,18\)) are symmetrically distributed. The number of dots for \(x = 10\) and \(x = 18\) are the same, for \(x = 11\) and \(x = 17\) are the same, for \(x = 12\) and \(x = 16\) are the same, and for \(x = 13\) and \(x = 15\) are the same.

Step3: Analyze option B

Option B is not symmetric. The left - hand side (values \(2,4,5\)) and the right - hand side (values \(9,10,11\)) do not form a mirror - image about a central value.

Step4: Analyze option C

Option C is not symmetric. The distribution of dots on the left - hand side (values \(1.2,1.3,1.4,1.5\)) and the right - hand side (values \(1.6,1.7,1.8\)) does not have a mirror - like property.

Step5: Analyze option D

Option D is not symmetric. The left - hand side (values \(10,11,12,13\)) and the right - hand side (values \(18,19\)) do not match in a symmetric fashion.

Answer:

A. Option A