The median from the following distribution is
`{:("Class" :,5-10,10-15,15-20,20-25,25-30,30-35,35-40,40-45),("Frequency":,5,6,15,10,5,4,2,2):}`

Options

A. 19
B. 19.5
C. 20
D. 18

Explanation

To find the median from the given frequency distribution, we will follow these steps:

### Step 1: Create a Cumulative Frequency Table
We start by organizing the data into a cumulative frequency table.

| Class | Frequency (f) | Cumulative Frequency (CF) |
|---------|---------------|---------------------------|
| 5-10 | 5 | 5 |
| 10-15 | 6 | 11 |
| 15-20 | 15 | 26 |
| 20-25 | 10 | 36 |
| 25-30 | 5 | 41 |
| 30-35 | 4 | 45 |
| 35-40 | 2 | 47 |
| 40-45 | 2 | 49 |

### Step 2: Calculate Total Frequency (N)
The total frequency (N) is the sum of all frequencies.

\[ N = 5 + 6 + 15 + 10 + 5 + 4 + 2 + 2 = 49 \]

### Step 3: Find \( N/2 \)
Next, we calculate \( N/2 \):

\[ N/2 = 49/2 = 24.5 \]

### Step 4: Identify the Median Class
We need to find the median class, which is the class where the cumulative frequency is greater than or equal to \( N/2 \).

From the cumulative frequency table, we see that the cumulative frequency just greater than 24.5 is 26, which corresponds to the class 15-20. Thus, the median class is 15-20.

### Step 5: Identify the Values Needed for the Median Formula
- **Lower boundary (l)** of the median class (15-20) = 15
- **Frequency (f)** of the median class = 15
- **Cumulative frequency (F)** of the class preceding the median class (10-15) = 11
- **Class width (h)** = 5 (the difference between the upper and lower boundaries of the class)

### Step 6: Apply the Median Formula
The formula for the median is given by:

\[ \text{Median} = l + \left( \frac{N/2 - F}{f} \right) \times h \]

Substituting the values we have:

\[ \text{Median} = 15 + \left( \frac{24.5 - 11}{15} \right) \times 5 \]

### Step 7: Calculate the Median
Calculating the expression inside the parentheses:

\[ \frac{24.5 - 11}{15} = \frac{13.5}{15} = 0.9 \]

Now, substituting this back into the median formula:

\[ \text{Median} = 15 + (0.9 \times 5) = 15 + 4.5 = 19.5 \]

### Final Answer
Thus, the median of the given frequency distribution is **19.5**.

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