To find the mean, standard deviation, and variance of Lucas's lunch expenditures, we first need to calculate the mean.
1. Calculate the mean:
Mean = (4.85 + 5.10 + 5.50 + 4.75 + 4.50 + 5.00 + 6.00) / 7
Mean = 35.70 / 7
Mean = 5.1
So, the mean expenditure on lunch for Lucas is $5.10.
2. Calculate the standard deviation:
a. Calculate the variance:
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 = 1.4725 / 7
Variance ≈ 0.210
b. Calculate the standard deviation:
Standard Deviation = √Variance
Standard Deviation = √0.210
Standard Deviation ≈ 0.458
So, the standard deviation of Lucas's lunch expenditures is approximately $0.458.
Therefore, the mean expenditure is $5.10, the standard deviation is approximately $0.458, and the variance is approximately $0.210.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
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.
1 answer
52 answers