For the following frequency distribution, find the median (accurate to 4 decimal places):

Data Value

Frequency

1.8

22

6.8

5

8.6

6

To find the median for a frequency distribution, we first need to determine the cumulative frequency and then locate the median class.

### Step 1: Organize the data

| Data Value | Frequency |
|------------|-----------|
| 1.8        | 22        |
| 6.8        | 5         |
| 8.6        | 6         |

### Step 2: Calculate the cumulative frequency

| Data Value | Frequency | Cumulative Frequency |
|------------|-----------|----------------------|
| 1.8        | 22        | 22                   |
| 6.8        | 5         | 27                   |
| 8.6        | 6         | 33                   |

### Step 3: Determine the median position

The median is located at the \( \frac{N+1}{2} \)th position, where \( N \) is the total number of data points.

Total \( N = 22 + 5 + 6 = 33 \)

Median position = \( \frac{33 + 1}{2} = \frac{34}{2} = 17 \)th position

### Step 4: Identify the median class

The 17th data point falls within the cumulative frequency of 22, which corresponds to the data value 1.8.

### Step 5: Calculate the exact median

Since the 17th position is within the first class (1.8), and the data is discrete, the median value is exactly **1.8**.

Thus, the median value is **1.8000** (accurate to four decimal places).

Would you like more details or have any questions?

Here are some related questions:
1. How would you find the mode of this frequency distribution?
2. What is the mean of this frequency distribution?
3. How can you determine the range of the data?
4. What is the importance of finding the cumulative frequency in this context?
5. How can you use this frequency distribution to create a histogram?

**Tip:** The median is a robust measure of central tendency, especially useful when your data is skewed.

Learn how to find the median of a frequency distribution with a detailed step-by-step guide. This problem involves calculating the median from a given frequency distribution table, understanding cumulative frequency, and determining the exact median value. Suitable for high school students.

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