The following data represent the dividend yields​ (in percent) of a random sample of 28 publicly traded stocks.
2.31
0.15
2.82
0.53
0.02
2.61
1.4
0.76
0
1.94
0
0.84
3.19
0.48
0.38
3.54
1.08
0.12
2.14
3.07
0
0.1
0
0.8
2.98
0.99
0.64
2.08
​(a) Compute the​ five-number summary.

To compute the five-number summary of the dividend yields, we need to find the following values:

1. **Minimum**: The smallest value in the dataset.
2. **First quartile (Q1)**: The value at the 25th percentile of the dataset.
3. **Median (Q2)**: The value at the 50th percentile of the dataset.
4. **Third quartile (Q3)**: The value at the 75th percentile of the dataset.
5. **Maximum**: The largest value in the dataset.

### Step-by-Step Calculation:

1. **Arrange the data in ascending order:**
   \[
   0, 0, 0, 0, 0.02, 0.1, 0.12, 0.15, 0.38, 0.48, 0.53, 0.64, 0.76, 0.8, 0.84, 0.99, 1.08, 1.4, 1.94, 2.08, 2.14, 2.31, 2.61, 2.82, 2.98, 3.07, 3.19, 3.54
   \]

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

3. **First quartile (Q1)**: To find the first quartile, we locate the value at the 25th percentile. For a dataset of 28 numbers:
   \[
   Q1 = \text{Value at position} \left(\frac{28+1}{4}\right) = \text{Value at position 7.25} \approx \text{Value between 7th and 8th values.}
   \]
   The 7th and 8th values are \(0.12\) and \(0.15\), so:
   \[
   Q1 \approx \frac{0.12 + 0.15}{2} = 0.135.
   \]

4. **Median (Q2)**: The median is the value at the 50th percentile:
   \[
   Q2 = \text{Value at position} \left(\frac{28+1}{2}\right) = \text{Value at position 14.5}.
   \]
   The 14th and 15th values are \(0.8\) and \(0.84\), so:
   \[
   Q2 \approx \frac{0.8 + 0.84}{2} = 0.82.
   \]

5. **Third quartile (Q3)**: To find the third quartile, locate the value at the 75th percentile:
   \[
   Q3 = \text{Value at position} \left(3 \times \frac{28+1}{4}\right) = \text{Value at position 21.75}.
   \]
   The 21st and 22nd values are \(2.14\) and \(2.31\), so:
   \[
   Q3 \approx \frac{2.14 + 2.31}{2} = 2.225.
   \]

6. **Maximum**: The largest value is \(3.54\).

### The Five-Number Summary:

- **Minimum**: \(0\)
- **First quartile (Q1)**: \(0.135\)
- **Median (Q2)**: \(0.82\)
- **Third quartile (Q3)**: \(2.225\)
- **Maximum**: \(3.54\)

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Do you want more details or have any questions? 

Here are 5 related questions for further exploration:

1. How would the interquartile range (IQR) be calculated from this dataset?
2. What does the shape of the data distribution suggest based on this five-number summary?
3. How could outliers be detected using this five-number summary?
4. What impact would additional data points have on the quartiles and median?
5. How can the five-number summary be visually represented?

**Tip:** The interquartile range (IQR) is a useful measure for detecting the spread of the middle 50% of data points in a dataset.

The following data represent the dividend yields​ (in percent) of a random sample of 28 publicly traded stocks. (a) Compute the​ five-number summary.

Learn how to compute the five-number summary for a dataset of 28 dividend yields from publicly traded stocks. This problem covers key statistical concepts, including the calculation of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Suitable for students in Grades 9-12.

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