`{:("Class Interval",0.10,10-20,20-30,30-40,40-50),("Frequency",5,0,20,5,10):}`
What is the median of the above frequency distribution?

Options

A. 23
B. 24
C. 25
D. 26

Explanation

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

### Step 1: Write down the class intervals and their corresponding frequencies.
- Class Intervals: 0-10, 10-20, 20-30, 30-40, 40-50
- Frequencies: 5, 0, 20, 5, 10

### Step 2: Calculate the cumulative frequency.
- Cumulative Frequency (CF):
- For 0-10: CF = 5
- For 10-20: CF = 5 + 0 = 5
- For 20-30: CF = 5 + 20 = 25
- For 30-40: CF = 25 + 5 = 30
- For 40-50: CF = 30 + 10 = 40

So, the cumulative frequencies are:
- 0-10: 5
- 10-20: 5
- 20-30: 25
- 30-40: 30
- 40-50: 40

### Step 3: Find the total frequency (n).
- Total Frequency (n) = 40

### Step 4: Calculate n/2.
- n/2 = 40/2 = 20

### Step 5: Identify the median class.
- The cumulative frequency just greater than 20 is 25, which corresponds to the class interval 20-30. Therefore, the median class is 20-30.

### Step 6: Apply the median formula.
The formula for the median in a grouped frequency distribution is:
\[ \text{Median} = L + \left( \frac{n/2 - CF}{f} \right) \times h \]
Where:
- \( L \) = lower limit of the median class = 20
- \( n/2 \) = 20
- \( CF \) = cumulative frequency of the class preceding the median class = 5 (for class 10-20)
- \( f \) = frequency of the median class = 20 (for class 20-30)
- \( h \) = width of the median class = 10 (for class 20-30)

### Step 7: Substitute the values into the formula.
\[ \text{Median} = 20 + \left( \frac{20 - 5}{20} \right) \times 10 \]
\[ = 20 + \left( \frac{15}{20} \right) \times 10 \]
\[ = 20 + 7.5 \]
\[ = 27.5 \]

### Conclusion:
The median of the given frequency distribution is **27.5**.

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