SOLUTION: 2. Then grade point averages of 20 college students selected at random from the graduating class are as follows: 3.2 1.9 2.7 2.4 2.8 2.9 3.8 3.0 2.5 3.3 1.8 2.5 3.7 2.8

Question 1191696: 2. Then grade point averages of 20 college students selected at random from the graduating class are as follows:
3.2 1.9 2.7 2.4
2.8 2.9 3.8 3.0
2.5 3.3 1.8 2.5
3.7 2.8 2.0 3.2
2.3 2.1 2.5 1.9
a. Calculate the descriptive statistics.
b. Use the appropriate graph for the GPA of the 20 students.

Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's the solution:
**a. Descriptive Statistics**
First, let's organize the data in ascending order to make calculations easier:
1.8, 1.9, 1.9, 2.0, 2.1, 2.3, 2.4, 2.5, 2.5, 2.5, 2.7, 2.8, 2.8, 2.9, 3.0, 3.2, 3.2, 3.3, 3.7, 3.8
Now we can calculate the descriptive statistics:
* **Mean:** (Sum of all values) / (Number of values)
Mean = (1.8 + 1.9 + 1.9 + 2.0 + 2.1 + 2.3 + 2.4 + 2.5 + 2.5 + 2.5 + 2.7 + 2.8 + 2.8 + 2.9 + 3.0 + 3.2 + 3.2 + 3.3 + 3.7 + 3.8) / 20
Mean = 51.5 / 20 = 2.575
* **Median:** The middle value (since there are 20 values, the median is the average of the 10th and 11th values)
Median = (2.5 + 2.7) / 2 = 2.6
* **Mode:** The most frequent value(s)
Mode = 2.5 (appears 3 times)
* **Range:** Maximum value - Minimum value
Range = 3.8 - 1.8 = 2.0
* **Variance:** The average of the squared differences from the mean. Here's how to calculate it:
1. Subtract the mean from each value and square the result.
2. Sum all the squared differences.
3. Divide the sum by the number of values minus 1 (n-1 = 20-1 =19 for sample variance). This is called the sample variance.
Variance ≈ 0.355 (You can use a calculator or spreadsheet software for this).
* **Standard Deviation:** The square root of the variance
Standard Deviation ≈ √0.355 ≈ 0.596
**b. Appropriate Graph**
A **histogram** or a **stem-and-leaf plot** would be appropriate for visualizing the GPA data. A histogram is generally preferred for larger datasets. Here's what a histogram would look like conceptually:
* **X-axis:** GPA ranges (e.g., 1.8-2.0, 2.0-2.2, 2.2-2.4, ..., 3.8-4.0)
* **Y-axis:** Frequency (number of students in each GPA range)
You would then create bars for each GPA range, with the height of the bar representing the number of students whose GPAs fall within that range.
A stem-and-leaf plot would also be suitable, especially since the dataset is relatively small. It would show the individual data points while still giving a sense of the distribution. Here's how it would look:
```
1 | 899
2 | 01345557889
3 | 022378
```
Where the "stem" is the digit before the decimal point, and the "leaves" are the digits after the decimal point.
Both the histogram and stem-and-leaf plot would give you a visual representation of the distribution of GPAs among the 20 students.

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