Lucas recorded his lunch expenditure each day for one week in the table below. Day S M T W T F SExpenditure $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.

The mean is 5.10.  The standard deviation is 0.467.  The variance is 0.218.

The mean is found by adding all of the data points and dividing by the number of data points, 7:

(4.85+5.10+5.50+4.75+4.50+5.00+6.00)/7 = 5.10.

The variance is found by finding the difference between each data point and the mean, squaring it, and averaging them together:

[(4.85-5.1)²+(5.1-5.1)²+(5.5-5.1)²+(4.75-5.1)²+(4.5-5.1)²+(5-5.1)²+(6-5.1)²]/7 =
[(-0.25)²+0²+0.4²+(-0.35)²+(-0.6)²+(-0.1)²+0.9²]/7
= (0.0625+0+0.16+0.1225+0.36+0.01+0.81)/7 = 1.525/7 = 0.218

The standard deviation is the square root of the variance:
√0.218 = 0.467