Vitamin D Seizures Cea8Ac
1. **State the problem:** We need to analyze maternal blood vitamin D levels in two groups of breastfed infants: those with seizures and those without seizures, based on box-and-whisker plots.
2. **Median comparison:** The median is the middle value of a dataset when ordered.
- From the plot, the median maternal blood vitamin D level for the "no seizures" group is approximately $35$ ng/mL.
- The median for the "seizures" group is approximately $10$ ng/mL.
This shows infants with seizures have a much lower median maternal blood vitamin D level.
3. **Interquartile Range (IQR):** IQR is $Q3 - Q1$, representing the middle 50% of data.
- For "no seizures": $Q1 \approx 25$, $Q3 \approx 45$, so $IQR = 45 - 25 = 20$ ng/mL.
- For "seizures": $Q1 \approx 5$, $Q3 \approx 15$, so $IQR = 15 - 5 = 10$ ng/mL.
The "seizures" group has a smaller IQR, indicating less spread in vitamin D levels.
4. **Upper range outlier for "seizures":** Outliers are values beyond $Q3 + 1.5 \times IQR$.
Calculate upper fence:
$$Q3 + 1.5 \times IQR = 15 + 1.5 \times 10 = 15 + 15 = 30$$
Any value above $30$ ng/mL in the "seizures" group is an upper outlier.
5. **Percentage below 9 ng/mL in "seizures":**
- The box plot shows the lower whisker near $0$ and $Q1$ at $5$.
- Values below $9$ ng/mL lie between $0$ and $9$.
- Since $Q1$ is $5$ and median is $10$, roughly half the data is below median.
- The portion below $9$ is slightly less than half of the group.
Estimating percentage:
- Approximately $40\%$ of infants in the "seizures" group have maternal blood vitamin D levels below $9$ ng/mL.
**Final answers:**
- Median no seizures: $35$ ng/mL
- Median seizures: $10$ ng/mL
- IQR no seizures: $20$ ng/mL
- IQR seizures: $10$ ng/mL
- Upper outlier threshold seizures: above $30$ ng/mL
- Percentage below $9$ ng/mL seizures: approximately $40\%$