Lucas recorded his lunch expenditure each day for one week in the table below. Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Expenditure $4.85 $5.10 $5.50 $4.75 $4.50 $5.00 $6.00 Find the mean, standard deviation, and variance of Lucas’s lunch expenditures. Round to the nearest thousandth. (3 points)

Answer 1

To find the mean, standard deviation, and variance of Lucas's lunch expenditures, we first need to calculate the total expenditure for the week, the mean, and then use those values to find the standard deviation and variance.

Total Expenditure:
$4.85 + $5.10 + $5.50 + $4.75 + $4.50 + $5.00 + $6.00 = $35.70

Mean:
Mean = Total Expenditure / Number of Days
Mean = $35.70 / 7
Mean = $5.1 (rounded to the nearest tenth)

Variance:
Variance = Σ (x - μ)² / n
where x = individual expenditure, μ = mean expenditure, and n = number of observations

Variance = [$4.85 - $5.1)² + ($5.10 - $5.1)² + ($5.50 - $5.1)² + ($4.75 - $5.1)² + ($4.50 - $5.1)² + ($5.00 - $5.1)² + ($6.00 - $5.1)²] / 7
Variance = [($0.25)² + ($0.00)² + ($0.40)² + ($0.35)² + ($0.60)² + ($0.10)² + ($0.90)²] / 7
Variance = [$0.0625 + $0.1600 + $0.1225 + $0.3600 + $0.0100 + $0.8100] / 7
Variance = $1.525 / 7
Variance = 0.218 (rounded to the nearest thousandth)

Standard Deviation:
Standard Deviation = √Variance
Standard Deviation = √0.218
Standard Deviation ≈ 0.467 (rounded to the nearest thousandth)

Therefore, the mean expenditure is $5.1, the variance is 0.218, and the standard deviation is approximately 0.467.