Question:medium
Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).
Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).
Updated On: Jan 13, 2026
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Solution and Explanation
\(\text{The formula for Variance is:}\) \(\frac{\sum x^2}{n}-(\bar x)^2\)
\(\text{Using the provided data, we calculate:}\)
\(\frac{7200+1936+3364+4624+3136+\alpha^2+\beta^2}{8}-3364\) \(=66.2\)
\(2532.5+\frac{\alpha^2+\beta^2}{8}-3364=66.2\)
\(=7181.6\) \(\approx7182\)
\(\text{The final answer is 7182.}\)
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