The following data represent the dividend yields​ (in percent) of a random sample of 28 publicly traded stocks. Complete parts ​(a) to​ (c).
2.892.89
0.080.08
1.561.56
0.180.18
0.410.41
2.622.62
0.160.16
1.661.66
0.410.41
1.911.91
00
00
2.892.89
0.380.38
2.512.51
3.683.68
2.382.38
0.480.48
1.541.54
3.183.18
00
0.40.4
00
1.281.28
0.980.98
0.360.36
2.752.75
2.882.88
 
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Part 1
​(a) Compute the​ five-number summary.
The​ five-number summary is  enter your response here​,  enter your response here​,  enter your response here​,  enter your response here​,  enter your response here.
​(Round to two decimal places as needed. Use ascending​ order.)

To compute the five-number summary, we need to calculate the following values from the dataset:

1. **Minimum**: The smallest value in the dataset.
2. **First quartile (Q1)**: The median of the lower half of the data (excluding the overall median if the number of data points is odd).
3. **Median (Q2)**: The middle value of the dataset.
4. **Third quartile (Q3)**: The median of the upper half of the data.
5. **Maximum**: The largest value in the dataset.

### Steps:
1. **Sort the data in ascending order**:
   \[
   0, 0, 0, 0, 0.08, 0.16, 0.18, 0.36, 0.38, 0.4, 0.41, 0.41, 0.48, 0.98, 1.28, 1.54, 1.56, 1.66, 1.91, 2.38, 2.51, 2.62, 2.75, 2.88, 2.89, 2.89, 3.18, 3.68
   \]
   The dataset has 28 values.

2. **Minimum**: The smallest value is \(0\).

3. **First Quartile (Q1)**:
   To find Q1, locate the median of the lower half (the first 14 values):
   \[
   0, 0, 0, 0, 0.08, 0.16, 0.18, 0.36, 0.38, 0.4, 0.41, 0.41, 0.48, 0.98
   \]
   The median of these 14 values is the average of the 7th and 8th values:
   \[
   \text{Q1} = \frac{0.18 + 0.36}{2} = 0.27
   \]

4. **Median (Q2)**:
   The overall median is the average of the 14th and 15th values:
   \[
   \text{Q2} = \frac{0.98 + 1.28}{2} = 1.13
   \]

5. **Third Quartile (Q3)**:
   To find Q3, locate the median of the upper half (the last 14 values):
   \[
   1.28, 1.54, 1.56, 1.66, 1.91, 2.38, 2.51, 2.62, 2.75, 2.88, 2.89, 2.89, 3.18, 3.68
   \]
   The median of these 14 values is the average of the 7th and 8th values:
   \[
   \text{Q3} = \frac{2.51 + 2.62}{2} = 2.57
   \]

6. **Maximum**: The largest value is \(3.68\).

### The five-number summary is:
\[
\boxed{0, 0.27, 1.13, 2.57, 3.68}
\]

Would you like details on how to calculate these, or do you have other questions?

---

Here are 5 questions related to this:

1. How can the five-number summary help describe the distribution of data?
2. What is the significance of the interquartile range (IQR), and how would you compute it from the five-number summary?
3. How can you identify outliers using the five-number summary?
4. What is the relationship between the median and the mean in a skewed dataset?
5. How do boxplots visually represent the five-number summary?

**Tip:** To better understand the spread of data, focus on how far the quartiles are from each other—this helps measure variability.

The following data represent the dividend yields (in percent) of a random sample of 28 publicly traded stocks. Complete parts (a) to (c). 2.89, 0.08, 1.56, 0.18, 0.41, 2.62, 0.16, 1.66, 0.41, 1.91, 0, 0, 2.89, 0.38, 2.51, 3.68, 2.38, 0.48, 1.54, 3.18, 0, 0.40, 0, 1.28, 0.98, 0.36, 2.75, 2.88 (a) Compute the five-number summary.

Learn how to compute the five-number summary for a sample of dividend yields from 28 publicly traded stocks. Understand how to calculate the minimum, first quartile, median, third quartile, and maximum. Suitable for students in Grades 9-12.

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