To find the mean, standard deviation, and variance of Lucas's lunch expenditures, 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
Next, we calculate the mean:
Mean = Total expenditure / Number of days
Mean = $35.70 / 7
Mean = $5.100
Now, we calculate the variance. To do this, we first find the squared differences between each day's expenditure and the mean, then calculate the sum of these squared differences:
Squaring differences:
(Sunday - Mean)^2 = ($4.85 - $5.100)^2 = $0.0256
(Monday - Mean)^2 = ($5.10 - $5.100)^2 = $0.0000
(Tuesday - Mean)^2 = ($5.50 - $5.100)^2 = $0.2025
(Wednesday - Mean)^2 = ($4.75 - $5.100)^2 = $0.1102
(Thursday - Mean)^2 = ($4.50 - $5.100)^2 = $0.3600
(Friday - Mean)^2 = ($5.00 - $5.100)^2 = $0.0100
(Saturday - Mean)^2 = ($6.00 - $5.100)^2 = $0.8100
Sum of squared differences = $0.0256 + $0.0000 + $0.2025 + $0.1102 + $0.3600 + $0.0100 + $0.8100
Sum of squared differences = $1.5183
Variance = Sum of squared differences / (Number of days - 1)
Variance = $1.5183 / 6
Variance = $0.253
Finally, we calculate the standard deviation, which is the square root of the variance:
Standard deviation = √Variance
Standard deviation = √$0.253
Standard deviation = $0.503
Therefore, the mean of Lucas's lunch expenditures is $5.100, the variance is $0.253, and the standard deviation is $0.503.
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.
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