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

Question

Sunday $4.55, Monday $5.25, Tuesday $5.74, Wednesday $4.30, Thursday $4.20, Friday $5.60, Saturday $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 add up all the expenditures and divide by the number of days:

Mean = (4.55 + 5.25 + 5.74 + 4.3 + 4.2 + 5.6 + 6) / 7 = 5.036

So the mean cost of Lucas's lunch for the week was $5.036.

To find the standard deviation and variance, we'll need to use the following formulas:

σ = sqrt((Σ(xi - μ)^2) / n)

σ^2 = (Σ(xi - μ)^2) / n

Where:

σ is the standard deviation
σ^2 is the variance
Σ is the sum of
xi is the value of each expenditure
μ is the mean
n is the number of expenditures (in this case, n=7)

Using these formulas, we can calculate:

Standard deviation:

σ = sqrt(((4.55 - 5.036)^2 + (5.25 - 5.036)^2 + (5.74 - 5.036)^2 + (4.3 - 5.036)^2 + (4.2 - 5.036)^2 + (5.6 - 5.036)^2 + (6 - 5.036)^2) / 7) = 0.815

So the standard deviation of Lucas's lunch expenditures was $0.815.

Variance:

σ^2 = ((4.55 - 5.036)^2 + (5.25 - 5.036)^2 + (5.74 - 5.036)^2 + (4.3 - 5.036)^2 + (4.2 - 5.036)^2 + (5.6 - 5.036)^2 + (6 - 5.036)^2) / 7 = 0.664

So the variance of Lucas's lunch expenditures was $0.664^2.

Rounded to the nearest thousandth, the mean is $5.036, the standard deviation is $0.815, and the variance is $0.664.