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To determine whether there are outliers in the data, we need to calculate the Interquartile Range (IQR) and then use it to identify any potential outliers.

### Step 1: Calculate the IQR
The IQR is given by the difference between the third quartile (Q3) and the first quartile (Q1):
\[
\text{IQR} = Q3 - Q1 = 63 - 40 = 23
\]

### Step 2: Define the outlier bounds
- **Lower Bound** = \( Q1 - 1.5 \times \text{IQR} = 40 - 1.5 \times 23 = 40 - 34.5 = 5.5 \)
- **Upper Bound** = \( Q3 + 1.5 \times \text{IQR} = 63 + 1.5 \times 23 = 63 + 34.5 = 97.5 \)

Any data point below 5.5 or above 97.5 is considered an outlier.

### Step 3: Check the data
- **Minimum** = 4 (which is below the lower bound of 5.5, so it's an outlier).
- **Maximum** = 82 (which is within the upper bound of 97.5, so it's not an outlier).

Thus, there is at least one outlier that is too small, which matches the selected answer.

---

### Part c: Z-score Calculation
The z-score formula is:
\[
z = \frac{X - \mu}{\sigma}
\]
Where:
- \( X \) is the subject's data point.
- \( \mu \) is the mean.
- \( \sigma \) is the standard deviation.

Since the reduction in symptoms was **2 standard deviations greater than the average**, the z-score is simply **2.00**.

---

Would you like more details or have any questions about these steps?

Here are 5 related questions to consider:
1. How do you interpret the IQR in a five-number summary?
2. What happens if a data point is exactly on the outlier boundary?
3. How can the IQR method be applied to non-symmetrical distributions?
4. Why might there be only a lower outlier but no upper outlier in this dataset?
5. How do z-scores help compare data from different distributions?

**Tip**: When using z-scores, a positive score indicates a value above the mean, and a negative score indicates one below the mean.

The success of the drug was measured by the percent reduction in symptoms among the subjects. A five-number summary for the 'new drug' treatment group is given: 

Minimum: 4
First Quartile: 40
Median: 51
Third Quartile: 63
Maximum: 82

Are there any outliers in the data?

One subject showed a reduction in symptoms that was 2 standard deviations greater than average. Find the z-score for that subject.

Learn how to identify outliers in a dataset using the interquartile range (IQR) method and calculate a z-score. This problem includes a five-number summary and explains how to calculate outliers and interpret a z-score in a statistical context. Suitable for high school students in Grades 9-12.

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