To solve for the values of $ p $ and $ q $ with the given data, we can follow these steps:

### 1. Break Down the Problem
We need to find the values of $ p $ and $ q $ based on the information given about the mean and the total frequency. We can assume that we have a distribution table where frequencies are represented in terms of $ p $ and $ q $.

### 2. Relevant Concepts
The mean ($ \mu $) of a frequency distribution can be calculated using the formula:
$$
\mu = \frac{\sum fx}{\sum f}
$$
where:
- $ f $ is the frequency,
- $ x $ represents the mid-value of classes.

We know:
- Mean = 50
- Total frequency ($ \sum f $) = 120

Let’s assume the frequencies can be represented as:
- Frequency 1 = $ p $
- Frequency 2 = $ q $
- Other frequencies can be represented or accounted for.

Thus, we have:
$$
p + q + \text{(other frequencies)} = 120
$$

### 3. Analysis and Detail
Since we don't have the precise distribution values, we can organize our known quantities. For simplification, let's say other frequencies equal some constant $ k $. Thus we can express the total frequency as:
$$
p + q + k = 120
$$

For the mean, we would calculate the numerator:
$$
\sum fx = 50 \cdot 120 = 6000
$$

### 4. Verification and Summarize
From the above setup, we can set up equations that relate $ p $ and $ q $ to the mean.

Assuming that the mid-values of classes are known or can be defined, we would sum the products of frequencies and their respective mid-values, equate it to 6000, and solve for $ p $ and $ q $.

If we were given specific numerical values or a clearer distribution, we could derive explicit numbers for $ p $ and $ q $. Without that, we can indicate a relationship rather than exact solutions.

### Final Answer
To find specific values for $ p $ and $ q $, we would need additional information, such as frequencies for specific classes or more data belonging to the frequency distribution. If you provide the specific distribution or additional equations, I can help solve for $ p $ and $ q $ specifically.

Question

To solve for the values of $ p $ and $ q $ with the given data, we can follow these steps:

### 1. Break Down the Problem
We need to find the values of $ p $ and $ q $ based on the information given about the mean and the total frequency. We can assume that we have a distribution table where frequencies are represented in terms of $ p $ and $ q $.

### 2. Relevant Concepts
The mean ($ \mu $) of a frequency distribution can be calculated using the formula:
$$
\mu = \frac{\sum fx}{\sum f}
$$
where:
- $ f $ is the frequency,
- $ x $ represents the mid-value of classes.

We know:
- Mean = 50
- Total frequency ($ \sum f $) = 120

Let’s assume the frequencies can be represented as:
- Frequency 1 = $ p $
- Frequency 2 = $ q $
- Other frequencies can be represented or accounted for.

Thus, we have:
$$
p + q + \text{(other frequencies)} = 120
$$

### 3. Analysis and Detail
Since we don't have the precise distribution values, we can organize our known quantities. For simplification, let's say other frequencies equal some constant $ k $. Thus we can express the total frequency as:
$$
p + q + k = 120
$$

For the mean, we would calculate the numerator:
$$
\sum fx = 50 \cdot 120 = 6000
$$

### 4. Verification and Summarize
From the above setup, we can set up equations that relate $ p $ and $ q $ to the mean.

Assuming that the mid-values of classes are known or can be defined, we would sum the products of frequencies and their respective mid-values, equate it to 6000, and solve for $ p $ and $ q $.

If we were given specific numerical values or a clearer distribution, we could derive explicit numbers for $ p $ and $ q $. Without that, we can indicate a relationship rather than exact solutions.

### Final Answer
To find specific values for $ p $ and $ q $, we would need additional information, such as frequencies for specific classes or more data belonging to the frequency distribution. If you provide the specific distribution or additional equations, I can help solve for $ p $ and $ q $ specifically.

Knowee AI · Accepted Answer