Question
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.
Answers
GPT 3.5
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.
$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.