Fiona recorded the number of miles she biked each day last week as shown. 4 , 7 , 4 , 10 , 5 The mean is given by mu is equal to 6 Which equation shows the variance for the number of miles Fiona biked last week?
Answer
A
s is equal to square root of the fraction with numerator open paren 4 minus 6 close paren squared plus open paren 7 minus 6 close paren squared plus open paren 4 minus 6 close paren squared plus open paren 10 minus 6 close paren squared plus open paren 5 minus 6 close paren squared and denominator 4 end root
B
s squared is equal to the fraction with numerator open paren 4 minus 6 close paren squared plus open paren 7 minus 6 close paren squared plus open paren 4 minus 6 close paren squared plus open paren 10 minus 6 close paren squared plus open paren 5 minus 6 close paren squared and denominator 6
C
sigma squared is equal to the fraction with numerator open paren 4 minus 6 close paren squared plus open paren 7 minus 6 close paren squared plus open paren 4 minus 6 close paren squared plus open paren 10 minus 6 close paren squared plus open paren 5 minus 6 close paren squared and denominator 5
D
sigma is equal to square root of the fraction with numerator open paren 4 minus 6 close paren squared plus open paren 7 minus 6 close paren squared plus open paren 4 minus 6 close paren squared plus open paren 10 minus 6 close paren squared plus open paren 5 minus 6 close paren squared and denominator 5 end root
Explanation
Variance is the average of the squared differences from the mean. Since Fiona’s five recorded days are the full set being considered and the mean is written as μ, use population variance: σ² = [(4 − 6)² + (7 − 6)² + (4 − 6)² + (10 − 6)² + (5 − 6)²] ÷ 5. Choice C gives this equation; the square-root formulas calculate standard deviation, not variance.
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