Thank you for catching that! Let's carefully recalculate the median step-by-step.

### Step-by-step Recalculation for the Median:

The **median** is the middle value of an ordered data set. If the total number of observations is even, the median is the average of the two middle values.

#### Step 1: Calculate the Total Number of Observations
The total number of observations can be found by summing the frequencies:

\[
\text{Total Observations} = 1 + 4 + 2 + 3 + 10 = 20
\]

There are 20 observations in total, which is an even number.

#### Step 2: Determine the Median Position
Since there are 20 observations, the median will be the average of the 10th and 11th values.

#### Step 3: Find the Cumulative Frequency to Locate the 10th and 11th Values
Let's use the cumulative frequency table to identify the 10th and 11th values:

| Data | Frequency | Cumulative Frequency |
|------|-----------|----------------------|
| 27   | 1         | 1                    |
| 28   | 4         | 5                    |
| 29   | 2         | 7                    |
| 30   | 3         | 10                   |
| 31   | 10        | 20                   |

The 10th value is 30 (cumulative frequency is 10), and the 11th value is 31 (cumulative frequency is 11).

#### Step 4: Calculate the Median
The median is the average of the 10th and 11th values:

\[
\text{Median} = \frac{30 + 31}{2} = \frac{61}{2} = 30.5
\]

### Correct Median:

- **Median** = 30.5

Would you like further details or have any questions?

### Related Questions:

1. What are the first and third quartiles (Q1 and Q3) of this data set?
2. How do you calculate the interquartile range (IQR) for this data?
3. How would adding another data point of 32 affect the median?
4. What is the significance of the mean in comparison to the median in a skewed distribution?
5. Can there be more than one mode in a data set? If so, how is it called?

**Tip**: When working with frequency distributions, always verify positions using cumulative frequencies to avoid errors.

Learn how to recalculate the median correctly with step-by-step guidance. This problem involves understanding the concept of median in statistics and correcting a calculation error. Suitable for students in Grades 7-9.

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