The frequency of an observation p is q and the frequency of another observation q is p, then mean is_________

Answer

To find the mean of the observations given their frequencies, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Observations and Frequencies**:
- We have two observations: \( p \) and \( q \).
- The frequency of observation \( p \) is \( q \).
- The frequency of observation \( q \) is \( p \).

2. **Set Up the Frequency Table**:
- We can represent the observations and their frequencies as follows:
- Observation \( p \) with frequency \( q \).
- Observation \( q \) with frequency \( p \).

3. **Use the Mean Formula**:
- The formula for the mean (\( \bar{x} \)) in a frequency distribution is:
\[ \bar{x} = \frac{\sum (x_i \cdot f_i)}{\sum f_i} \]
- Here, \( x_i \) represents the observations and \( f_i \) represents their frequencies.

4. **Calculate the Numerator**:
- For our observations, the numerator will be:
\[ (p \cdot q) + (q \cdot p) = pq + qp = 2pq \]

5. **Calculate the Denominator**:
- The denominator, which is the total frequency, is:
\[ q + p \]

6. **Combine the Results**:
- Now, substituting the numerator and denominator into the mean formula, we have:
\[ \bar{x} = \frac{2pq}{p + q} \]

7. **Final Result**:
- Therefore, the mean of the observations is:
\[ \bar{x} = \frac{2pq}{p + q} \]

### Final Answer:
The mean is \( \frac{2pq}{p + q} \).