Compare the frequencies above and below the median class.

(a)
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Marks & $0-10$ & $10-20$ & $20-30$ & $30-40$ & $40-50$ & $50-60$ \\
\hline
Frequency & 10 & 8 & 6 & 12 & 5 & 9 \\
\hline
\end{tabular}
\][/tex]



Answer :

To compare the frequencies above and below the median class, let's first identify the key elements required for this comparison:

1. Total Frequency: This is the sum of all frequencies.
2. Median Frequency: This is half of the total frequency.
3. Median Class: This is the class interval in which the median frequency falls.
4. Frequency Below Median Class: This is the count of frequency entries below the median class.
5. Frequency Above Median Class: This is the count of frequency entries above the median class.

Given the table:

| Marks | [tex]$0-10$[/tex] | [tex]$0-20$[/tex] | [tex]$0-30$[/tex] | [tex]$0-40$[/tex] | [tex]$0-50$[/tex] | [tex]$0-60$[/tex] |
|-------|--------|--------|--------|--------|--------|--------|
| Frequency | 10 | 18 | 24 | 36 | 41 | 50 |

Let's proceed with the step-by-step solution:

### Step 1: Determine the Total Frequency

The total frequency is the cumulative frequency at the last class interval (`0-60`):
[tex]\[ \text{Total Frequency} = 50 \][/tex]

### Step 2: Determine the Median Frequency

The median frequency is half of the total frequency:
[tex]\[ \text{Median Frequency} = \frac{50}{2} = 25.0 \][/tex]

### Step 3: Determine the Median Class

The median class is the class interval where the cumulative frequency first exceeds the median frequency (25.0). Examining the cumulative frequencies:

- 10 (for [tex]$0-10$[/tex])
- 18 (for [tex]$0-20$[/tex])
- 24 (for [tex]$0-30$[/tex])
- 36 (for [tex]$0-40$[/tex]) — This is where the cumulative frequency first exceeds 25.0.

Thus, the median class is:
[tex]\[ \text{Median Class} = 0-40 \][/tex]

### Step 4: Count Frequencies Below the Median Class

The number of class intervals below the median class (`0-40`) is 3 (`[tex]$0-10$[/tex]`, `[tex]$0-20$[/tex]`, `[tex]$0-30$[/tex]`).

### Step 5: Count Frequencies Above the Median Class

The number of class intervals above the median class (`0-40`) is 2 (`[tex]$0-50$[/tex]`, `[tex]$0-60$[/tex]`).

### Conclusion

Let's summarize the findings:

- Total Frequency: 50
- Median Frequency: 25.0
- Median Class Index: 3 (corresponding to [tex]$0-40$[/tex])
- Median Class: [tex]$0-40$[/tex]
- Frequency Below Median Class: 3 intervals
- Frequency Above Median Class: 2 intervals

Comparing the frequencies:

- There are 3 class intervals below the median class.
- There are 2 class intervals above the median class.

Thus, there are more frequency class intervals below the median class than above the median class.

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