Find the median of the following data.
{:("Class Interval",f),(" "0-4,3)(" "4-8,6)(" "8-12,6),(" "12-16,6),(" "16-20,8):}

Options

A. 13
B. 12
C. 11
D. 10

Explanation

To find the median of the given grouped data, we will follow these steps:

### Step 1: Organize the Data
We have the following class intervals and their corresponding frequencies:

| Class Interval | Frequency (f) |
|----------------|----------------|
| 0 - 4 | 3 |
| 4 - 8 | 6 |
| 8 - 12 | 6 |
| 12 - 16 | 6 |
| 16 - 20 | 8 |

### Step 2: Calculate Cumulative Frequency
We will calculate the cumulative frequency (cf) for each class interval:

- For the first class (0 - 4): cf = 3
- For the second class (4 - 8): cf = 3 + 6 = 9
- For the third class (8 - 12): cf = 9 + 6 = 15
- For the fourth class (12 - 16): cf = 15 + 6 = 21
- For the fifth class (16 - 20): cf = 21 + 8 = 29

| Class Interval | Frequency (f) | Cumulative Frequency (cf) |
|----------------|----------------|----------------------------|
| 0 - 4 | 3 | 3 |
| 4 - 8 | 6 | 9 |
| 8 - 12 | 6 | 15 |
| 12 - 16 | 6 | 21 |
| 16 - 20 | 8 | 29 |

### Step 3: Calculate n
Now, we calculate the total frequency (n):

n = 3 + 6 + 6 + 6 + 8 = 29

### Step 4: Find n/2
Next, we calculate n/2:

n/2 = 29/2 = 14.5

### Step 5: Identify the Median Class
Now, we need to find the median class, which is the class interval where the cumulative frequency is greater than or equal to n/2 (14.5).

From our cumulative frequency table:
- The cumulative frequency just greater than 14.5 is 21, which corresponds to the class interval 12 - 16.

Thus, the median class is **12 - 16**.

### Step 6: Identify L, cf, f, and h
For the median class (12 - 16):
- L (lower limit of the median class) = 12
- cf (cumulative frequency of the previous class) = 15 (for class 8 - 12)
- f (frequency of the median class) = 6
- h (class width) = 4 (since 16 - 12 = 4)

### Step 7: Apply the Median Formula
Now we can use the median formula:

\[ \text{Median} = L + \left( \frac{n/2 - cf}{f} \right) \times h \]

Substituting the values:

\[ \text{Median} = 12 + \left( \frac{14.5 - 15}{6} \right) \times 4 \]

Calculating inside the parentheses:

\[ \text{Median} = 12 + \left( \frac{-0.5}{6} \right) \times 4 \]

Calculating:

\[ \text{Median} = 12 - \left( \frac{2}{6} \right) \]

\[ \text{Median} = 12 - \frac{1}{3} \]

\[ \text{Median} = 12 - 0.3333 \approx 11.6667 \]

Thus, the median is approximately **11.67**.

### Final Answer
The median of the given data is approximately **11.67**.

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