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.