ITPEC IP April 2023 Question 1
ITPEC IP April 2023 — Question 1 of 100
Histogram (d) has the largest variance because much of its frequency lies far from the center at both extremes. Variance averages squared distances from the mean, so observations far from the mean contribute disproportionately. Distribution (d) is U-shaped: it has relatively high frequency near the lowest and highest classes and relatively low frequency in the middle, producing the greatest spread around its mean.
Answer (d)
Why not others:
- (a) is skewed and spread out, but much of its mass is concentrated near one end
- (b) is broadly distributed but nearly uniform, with less emphasis on the extremes
- (c) concentrates most observations near the center, giving the smallest spread
Key rule: With comparable scales, variance grows when more observations lie farther from the mean, regardless of whether the distribution is symmetric.
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