Grace's entertainment expenses for the year were: $50 , $55 , $60 , $50 , $55 , $60 , $50 , $60 , $55 What is the standard deviation of her expenses? Use the following formula to calculate standard deviation: sigma is equal to square root of the fraction with numerator the sum from i is equal to 1 to n of open paren x sub i minus m close paren squared and denominator n end root where x sub i is each data point, and n is the number of data points.
The mean expense is $55, since the three values $50, $55, and $60 each occur three times. Each $50 or $60 is $5 from the mean, while each $55 is at the mean, so the squared deviations sum to 6 × 25 = 150. Divide by 9 and take the square root: √(150/9) ≈ $4.08, which is choice A.
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