For the distributions given below : Which of the following is correct for the…
2020
For the distributions given below :
Which of the following is correct for the above distributions ?
- A.
Standard deviation of A is significantly lower than standard deviation of B
- B.
Standard deviation of A is slightly lower than standard deviation of B
- C.
Standard deviation of A is same as standard deviation of B
- D.
Standard deviation of A is significantly higher than standard deviation of B
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Correct answer: C
First, analyze the frequency counts in each histogram. Distribution A shows frequencies decreasing from 5 to 1 as the values increase.
Distribution B shows frequencies increasing from 1 to 5 as the values increase.
The two distributions are mirror images of each other. This geometric symmetry means the spread of data points around the center is identical for both sets.
Since the variability or dispersion is the same, their standard deviations are equal.