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Lucas recorded his lunch expenditure each day for one week in the table below.
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.
To find the mean of Lucas's lunch expenditures, we need to sum up all the expenditures and then divide by the number of days:
Mean = Total Expenditure / Number of days
Mean = ($4.85 + $5.10 + $5.50 + $4.75 + $4.50 + $5.00 + $6.00) / 7
Mean = $35.70 / 7
Mean = $5.100
Now, to find the standard deviation, we need to first calculate the variance. To find the variance, we will:
1. Find the difference between each expenditure and the mean
2. Square each of those differences
3. Calculate the average of those squared differences
Variance = [(4.85 - 5.100)^2 + (5.10 - 5.100)^2 + (5.50 - 5.100)^2 + (4.75 - 5.100)^2 +
(4.50 - 5.100)^2 + (5.00 - 5.100)^2 + (6.00 - 5.100)^2] / 7
Variance = [(-0.250)^2 + (0.000)^2 + (0.400)^2 + (-0.350)^2 + (-0.600)^2 + (-0.100)^2 +
(0.900)^2] / 7
Variance = [0.0625 + 0.0000 + 0.1600 + 0.1225 + 0.3600 + 0.0100 + 0.8100] / 7
Variance = 1.525 / 7
Variance ≈ 0.218
Finally, to get the standard deviation, we take the square root of the variance:
Standard Deviation = √0.218
Standard Deviation ≈ 0.467
Therefore, the mean lunch expenditure is $5.100, the variance is approximately 0.218, and the standard deviation is approximately 0.467.