Lucas recorded his lunch expenditure each day for one week in the table below.

Question

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.

Answer 1

To find the mean, we first need to calculate 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

Now we can find the mean:

Mean = Total Expenditure / Number of days
Mean = $35.70 / 7
Mean = $5.10

To find the standard deviation:
1. Calculate the variance.
2. Take the square root of the variance.

Variance:
1. Calculate the squared difference between each expenditure and the mean, then sum these squared differences.
2. Divide by the 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 = [0.025^2 + 0^2 + 0.4^2 + 0.35^2 + 0.6^2 + 0.1^2 + 0.9^2] / 7
Variance = (0.000625 + 0 + 0.16 + 0.1225 + 0.36 + 0.01 + 0.81) / 7
Variance = 1.46225 / 7
Variance = 0.208892857

Standard Deviation = square root of Variance
Standard Deviation = √0.208892857
Standard Deviation ≈ 0.457

Therefore, the mean lunch expenditure is $5.10, the standard deviation is approximately 0.457, and the variance is approximately 0.209.