Enter your answer and show all the steps that you use to solve this problem in the space provided.Lucas recorded his lunch expenditure each day for one week in the table below.DaySundayMondayTuesday WednesdayThursdayFridaySaturdayExpenditure$4.85$5.10$5.50$4.75$4.50$5.00$6.00Find the mean, standard deviation, and variance of Lucas’s lunch expenditures. Round to the nearest thousandth.

Answer 1

To find the mean, standard deviation, and variance of Lucas's lunch expenditures, we first need to find the total expenditure for the week, then calculate the mean, standard deviation, and variance based on the data provided.

Step 1: Find the total expenditure for the week
Total expenditure = $4.85 + $5.10 + $5.50 + $4.75 + $4.50 + $5.00 + $6.00
Total expenditure = $35.70

Step 2: Find the mean
Mean = Total expenditure / Number of days
Mean = $35.70 / 7
Mean = $5.1

Step 3: Find the standard deviation
To find the standard deviation, we need to find the variance first.

Step 4: Find the variance
Variance = Σ(xi - mean)² / n
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)² + (0.4)² + (-0.35)² + (-0.6)² + (-0.1)² + (0.9)²] / 7
Variance = [0.0625 + 0 + 0.16 + 0.1225 + 0.36 + 0.01 + 0.81] / 7
Variance = 1.52 / 7
Variance = 0.2171

Step 5: Find the standard deviation
Standard deviation = √Variance
Standard deviation = √0.2171
Standard deviation ≈ 0.466

Therefore, the mean expenditure is $5.1, the standard deviation is approximately 0.466, and the variance is approximately 0.2171.