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.