Academia Aeternum
तमसो मा ज्योतिर्गमय
Wisdom · Knowledge · Eternity
Mean, Variance & Standard Deviation — Every Statistics Exercise Solved
3 exercise files · 29 total questions
\(\bar{x} = \dfrac{\sum x_i}{n};\quad \bar{x} = \dfrac{\sum f_i x_i}{\sum f_i}\)\(MD(\bar{x}) = \dfrac{\sum |x_i - \bar{x}|}{n}\)\(\sigma^2 = \dfrac{\sum(x_i-\bar{x})^2}{n} = \dfrac{\sum x_i^2}{n} - \bar{x}^2\)\(\sigma = \sqrt{\sigma^2};\quad CV = \dfrac{\sigma}{\bar{x}} \times 100\)Step 1 — Always compute mean x̄ first before any deviation formula. Step 2 — Set up a table: xᵢ | fᵢ | fᵢxᵢ | |xᵢ−x̄| | fᵢ|xᵢ−x̄| — fill column by column. Step 3 — For variance: use shortcut σ²=Σx²/n−(x̄)² to avoid squaring deviations. Step 4 — CV comparison: lower CV = more consistent distribution. Step 5 — Grouped data: always use class midpoint as xᵢ.
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