Question

Which of the following distributions is the most variable?

a. A distribution with μ=25 and σ=10.
b. A distribution with μ=15 and σ² =81.
c. A distribution with μ=40 and σ² =25.
d. A distribution with μ=25 and σ=7.

Answer 1

To find the most variable distribution, we compare the standard deviations. Distribution A with μ=25 and σ=10 has the highest standard deviation and is therefore the most variable.

Step-by-step explanation:

The variability of a distribution is measured by its standard deviation (or the square root of variance for those distributions expressed in terms of variance). To determine which distribution is the most variable, we look for the one with the highest standard deviation.

• Distribution A: Mean (μ) = 25, Standard Deviation (σ) = 10.
• Distribution B: Mean (μ) = 15, Variance (σ²) = 81, which yields a Standard Deviation (σ) of 9 (since σ = sqrt(σ²)).
• Distribution C: Mean (μ) = 40, Variance (σ²) = 25, which yields a Standard Deviation (σ) of 5 (since σ = sqrt(σ²)).
• Distribution D: Mean (μ) = 25, Standard Deviation (σ) = 7.

After calculating standard deviations from the given variances, we can see that Distribution A has the highest standard deviation and therefore is the most variable among the options provided.