Lucas recorded his lunch expenditure each day for one week in the table below. Day SundayMondayTuesday 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’ lunch expenditures. Round to the nearest thousandth.

Answer 1

To find the mean, standard deviation, and variance of Lucas' lunch expenditures, we first need to calculate the total expenditure for the week:

$4.85 + $5.10 + $5.50 + $4.75 + $4.50 + $5.00 + $6.00 = $35.70

Mean = total expenditure / number of days = $35.70 / 7 = $5.10

Next, we calculate the variance.

Variance = Σ(x - μ)² / n

where x = each day's expenditure, μ = mean expenditure, and n = number of days.

Variance = ($4.85 - $5.10)² + ($5.10 - $5.10)² + ($5.50 - $5.10)² + ($4.75 - $5.10)² + ($4.50 - $5.10)² + ($5.00 - $5.10)² + ($6.00 - $5.10)² / 7
Variance = $0.30² + $0.00² + $0.40² + $0.35² + $0.60² + $0.10² + $0.90² / 7
Variance = $0.0900 + $0.1600 + $0.1225 + $0.3600 + $0.0100 + $0.8100 + $0.0289 / 7
Variance = $1.5814 / 7
Variance = $0.2259

Lastly, we calculate the standard deviation, which is the square root of the variance:

Standard deviation = √$0.2259 ≈ $0.476

Therefore, the mean expenditure is $5.10, the variance is approximately $0.226, and the standard deviation is approximately $0.476.