Sample size and mean
Go to the Describing and Exploring Quantitative Variables tool at https://dcmathpathways.shinyapps.io/EDA_quantitative/.
Step 1) Select the Single Group tab.
Step 2) Locate the drop-down menu under Enter Data and select From Textbook.
Step 3) Locate the drop-down menu under Data Set and select Hurricane Damage.
In the descriptive statistics at the top of the applet, you will see the sample size [latex]\left(n\right)[/latex] and the mean [latex]\left(\bar{x}\right)[/latex] of the data set.
question 2
question 3
On the next page, you will continue to learn more about deviation from the mean.
Deviation from the mean
A deviation from the mean is the distance between an observation, [latex]x[/latex], in a data set and the mean, [latex]\bar{x}[/latex], of the data set. To calculate the deviation from the mean, subtract the sample mean from each observation in the data set [latex]\left(x-\bar{x}\right)[/latex].
Practice calculating the deviation from the mean in the following interactive example. Then, for the data table that follows, calculate the deviation from the mean to answer Question 4.
Example
Seven of [latex]50[/latex] observations a student made about her commute time by bicycle from her apartment to school are listed in the following table. Her mean commute time was [latex]10[/latex] minutes, [latex]\bar{x}=10[/latex]. Use this information to calculate the deviation from the mean [latex]\left(x-\bar{x}\right)[/latex] for each of the seven observations given.
Example: See the first entry in the table: an observed 8 minute commute time. Given a mean commute time of 10 minutes, the deviation from the mean for the observation of 8 minutes is [latex]8-10=-2[/latex].
Complete the table then check your answers below.
|
Bike Ride to School (in minutes) [latex]x[/latex] |
Deviation from the Mean (in minutes) [latex]x-\bar{x}[/latex] |
| 8 | [latex]8 - 10 = -2[/latex] |
| 10 | |
| 12 | |
| 14 | |
| 5 | |
| 15 | |
| 9 |
Now it’s your turn to calculate the deviation from the mean for ten of the 30 hurricane damage observations from the data set “Hurricane Damage.” Follow the instructions above to reopen the data set if you have closed it.
