1. **State the problem:** We have a data sample of size $n=6$ with values: 7, 4, 9, 7, 3, 12. 2. **Order the data:** Sort the data from smallest to largest: $$3, 4, 7, 7, 9, 12$$ 3. **Compute the first quartile (Q1):** Q1 is the median of the lower half (values below the overall median). The lower half is $3,4,7$. The median of $3,4,7$ is $4$ (middle value). 4. **Compute the third quartile (Q3):** Q3 is the median of the upper half (values above the overall median). The upper half is $7,9,12$. The median of $7,9,12$ is $9$ (middle value). 5. **Compute the interquartile range (IQR):** $$\text{IQR} = Q3 - Q1 = 9 - 4 = 5$$ 6. **Find the five-number summary:** - Minimum: $3$ - Q1: $4$ - Median (Q2): The median of the entire data set is the average of the 3rd and 4th values: $$\frac{7 + 7}{2} = 7$$ - Q3: $9$ - Maximum: $12$ 7. **Construct and describe the boxplot:** - The box spans from $Q1=4$ to $Q3=9$. - The median line is at $7$ inside the box. - Whiskers extend from the box to the minimum $3$ and maximum $12$. - The shape is roughly symmetric but slightly skewed right due to the larger maximum value. **Final answers:** - First quartile $Q1 = 4$ - Third quartile $Q3 = 9$ - Interquartile range $IQR = 5$ - Five-number summary: $3, 4, 7, 9, 12$ - Boxplot shape: approximately symmetric with slight right skewness.