Question

1 point
given the data sets below, rank them in order from the lowest to highest standard deviation
a = {100,100,100,100,100}
b = {-10, -7, 0, 9, 10}
c = {-2, -1, 0, 1, 2}

answer
a b c

Explanation:

Step1: Analyze Dataset A

All values in \( A = \{100, 100, 100, 100, 100\} \) are the same. The standard deviation (\( \sigma \)) of a dataset with all identical values is \( 0 \), since there is no variation.

Step2: Analyze Dataset C

For \( C = \{-2, -1, 0, 1, 2\} \), the values are symmetric around \( 0 \) and have small differences from the mean (which is \( 0 \)). The deviations from the mean are \( -2, -1, 0, 1, 2 \), and the squared deviations are \( 4, 1, 0, 1, 4 \). The variance is \( \frac{4 + 1 + 0 + 1 + 4}{5} = 2 \), so the standard deviation is \( \sqrt{2} \approx 1.414 \).

Step3: Analyze Dataset B

For \( B = \{-10, -7, 0, 9, 10\} \), the mean is \( \frac{-10 - 7 + 0 + 9 + 10}{5} = \frac{2}{5} = 0.4 \). The deviations from the mean are \( -10.4, -7.4, -0.4, 8.6, 9.6 \). Squaring these gives \( 108.16, 54.76, 0.16, 73.96, 92.16 \). The variance is \( \frac{108.16 + 54.76 + 0.16 + 73.96 + 92.16}{5} = \frac{329.2}{5} = 65.84 \), so the standard deviation is \( \sqrt{65.84} \approx 8.11 \).

Step4: Rank by Standard Deviation

Comparing the standard deviations: \( A \) (0) < \( C \) (≈1.414) < \( B \) (≈8.11).

Answer:

A, C, B