To determine if there are any outliers, we can use the interquartile range (IQR) method. Outliers are typically values that lie outside the range defined by:

$Q1 - 1.5 \times \text{IQR} \quad \text{and} \quad Q3 + 1.5 \times \text{IQR}$

Where:

• Q1 is the first quartile (the median of the lower half of the data).
• Q3 is the third quartile (the median of the upper half of the data).
• IQR is the difference between Q3 and Q1: $IQR = Q3 - Q1$.

Step 1: Organize the Data

The given grades are already in numerical order: 12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30.

Step 2: Find the Quartiles

• Q1 is the median of the first half of the data: The first half of the data is: 12, 14, 15, 16, 20, 22, 23, 23, 24, 24, 24, 25, 25, 25.
  Median of this subset = 23.

• Q3 is the median of the second half of the data: The second half of the data is: 25, 26, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30.
  Median of this subset = 27.

Step 3: Calculate the IQR

$IQR = Q3 - Q1 = 27 - 23 = 4$

Step 4: Determine the Outlier Boundaries

• Lower bound: $Q1 - 1.5 \times \text{IQR} = 23 - 1.5 \times 4 = 23 - 6 = 17$
• Upper bound: $Q3 + 1.5 \times \text{IQR} = 27 + 1.5 \times 4 = 27 + 6 = 33$

Step 5: Identify Outliers

Any values below 17 or above 33 are outliers. Looking at the data, the grades range from 12 to 30, so there are no values outside this range.

Conclusion:

There are no outliers in this data set.

So, the correct answer is: There are no outliers.

---

Would you like to explore how to calculate other statistical measures or do you have any questions about this solution?

---

Here are 5 related questions you might find interesting:

1. How do you calculate the median of a data set?
2. What is the significance of the IQR in detecting outliers?
3. How can you calculate the standard deviation of a data set?
4. What are the advantages of using a stemplot to visualize data?
5. How do you calculate the mean and compare it to the median?

Tip: When calculating quartiles, remember that if the number of data points is odd, the median is not included in either half of the data when calculating Q1 and Q3.