Question

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

Answer 1

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

Answer 2

Answer:

mean = 5.1

standard deviation = 0.47

variance = 0.22

Step-by-step explanation:

mean is average and to find it we add up all the numbers and then divide it by how many total numbers there are in the data set. $4.85 + $5.10 + $5.50 + $4.75 + $4.50 + $5.00 + $6.00 = $35.7. There are 7 different pieces of data, so 35.7/7= 5.1.

The mean would be 5.1

variance is how far spread out the numbers are and to find the first step is to take each number, subtract the mean from it, and then square it. Next we add all of the answers we got from this together, and divide them by data pieces. This sounds complicated but is really quite simple! So, $4.85 (our number) - 5.1 (our mean)= -0.25. Now take -0.25 and square it using a calculator (-0.25 x -0.25) which equals 0.0625. Now doing this for all the numbers:

4.85 - 5.10 = -0.25^2 = 0.0625

5.10 - 5.10 = 0^2 = 0

5.50 - 5.10 = 0.4^2 = 0.16

4.75 - 5.10 = 0.35^2 = 0.122

4.50 - 5.10 = 0.6^2 = 0.36

5.00 - 5.10 = 0.1^2 = 0.01

6.00 - 5.1 = 0.9^2 = 0.1225

all of these numbers should be positive at the end

Lets add all these up and divide the total to get our variance! 0.0625 + 0 + 0.16 + 0.122 + 0.36 + 0.01 + 0.1225 = 1.525. 1.525/7= 0.2179. Which rounds to 0.22 to the nearest tenth.

The variance would be 0.22.

standard deviation is how spread out the numbers are and to find it we take the square root of the variance. Our original variance is 0.2179 so punch into a calculator $\sqrt{.2179}$ = 0.466 which rounds to 0.47

The standard deviation would be 0.47

All the work is in bold :)