Question

Use this data in the problem below. Follow the steps carefully. Round to the nearest tenth.

Lot 3:

Week 1: 345 Week 2: 340 Week 3: 400 Week 4: 325

Step 1. Jim enters the data and calculates the average or mean.


Step 2. Jim calculates the deviation from the mean by subtracting the mean from each value.


Step 3. Jim squares each deviation to remove negative signs.


Step 4. Jim sums the squares of each deviation and divides by the count for the variance.


Step 5. Jim takes the square root of the variance to find the standard deviation.

Answer 1

`\bar X = (345+340+400+325)/(4)=352.5`

`\sigma = √(806.25)=28.395`

`s=√(1075)=32.787`

Explanation:

Week 1: 345 Week 2: 340 Week 3: 400 Week 4: 325

Step 1

In order to calculate the mean we need to use this formula:

`\bar X = (\sum_(i=1)^n X_i)/(n)`

And if we replace we got this:

`\bar X = (345+340+400+325)/(4)=352.5`

Step 2

We can calculate the deviation from the mean by subtracting the mean for each value like this:

Week 1: 345-352.5=-7.5

Week 2: 340-352.5=-12.5

Week 3: 400-352.5=47.5

Week 4: 325-352.5=-27.5

Step 3

Now we can square each deviation to remove the negative signs like this:

Week 1: 345-352.5=(-7.5)^2=56.26

Week 2: 340-352.5=(-12.5)^2=156.25

Week 3: 400-352.5=(47.5)^2=2256.25

Week 4: 325-352.5=(-27.5)^2=756.25

Step 4

Now we need to do this operation:

If we want to find the popularion deviation we need to divide by n

`(56.25+156.25+2256.25+756.25)/(4)=(3225)/(4)=806.25`

If we want to find the sample deviation we need to divide by n-1

`(56.25+156.25+2256.25+756.25)/(3)=(3225)/(3)=1075`

Step 5

Now we just need to take the root from step 4 in order to find the deviation:

`\sigma = √(806.25)=28.395`

`s=√(1075)=32.787`