9. Measures of Center, Spread, and Position
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Population data is information about every member of a given group, while sample data is information about a representative subset of the given group.
Data Type: Population
| Statistic | Class A | Class B |
|---|---|---|
| Range | 15 | 12 |
| Standard deviation | 3.8 | 3.3 |
| Variance | 14.2 | 10.9 |
Comparison: There is more variability in the population for Class A.
Considering the scenarios of the given data sets, let's first determine the type of data it is. Then we can analyze the range, standard deviation, and variability for both sets.
If a given data set is population data, the desired statistic is known for every member of the given group. If a given data set is sample data, the desired statistic is known for a small, representative portion of the given group.
In this case, we have been given the number of days each student missed this year. Because we have information about all students, the data set is population data.
To calculate the different statistical measures using a graphing calculator, we have to enter them into lists. We will do this by pressing the STAT button, selecting "Edit," and then entering the values into the first two lists.
Now that we entered the data, we will push STAT once more. Under "CALC," we will press ENTER once to select "1-Var Stats" and a second time to see statistical information about the first list, L1.
Note the output on the resulting screen. To determine the range, we look at the minimum and maximum values of the data set. Remember, variance is the square of the standard deviation. minX:& 0 maxX:& 15 Range:& 15-0=15 Sx:& 3.763 ≈ 3.8 (Sx)^2:& 3.763^2≈ 14.2 Let's repeat this process for the second list, L2. Once more, we press STAT and select "1-Var Stats" with ENTER. Before pressing ENTER again, we push 2nd and 2 to select L2.
Again, we can find all of the necessary information in the output. minX:& 1 maxX:& 13 Range:& 13-1=12 Sx:& 3.294 ≈ 3.3 (Sx)^2:& 3.294^2≈ 10.9
Now that we've found all of the necessary pieces of information from both of the data sets, we can compare the results. The standard deviation for Class A is 3.8 and 3.3 for Class B. Therefore, there is more variability in the population for Class A.