For a data containing 100 observations, the mean is 8. For 50 observations selected from these 100observations, the mean is 10. Find the mean of the other 50 observations.

Answer

To solve the problem step-by-step, we will follow the given information and apply the formula for the mean.

### Step 1: Understand the given data
We have:
- Total observations (n) = 100
- Mean of all observations (x̄) = 8
- Mean of 50 selected observations = 10

### Step 2: Calculate the total sum of the 100 observations
Using the formula for mean:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
We can rearrange this to find the sum of observations:
\[ \text{Sum of observations} = \text{Mean} \times \text{Number of observations} \]
For the 100 observations:
\[ \text{Sum of 100 observations} = 8 \times 100 = 800 \]

### Step 3: Calculate the total sum of the 50 selected observations
Using the same formula for the 50 observations:
\[ \text{Sum of 50 observations} = 10 \times 50 = 500 \]

### Step 4: Find the sum of the remaining 50 observations
To find the sum of the remaining 50 observations, we subtract the sum of the selected 50 observations from the total sum of the 100 observations:
\[ \text{Sum of remaining 50 observations} = \text{Sum of 100 observations} - \text{Sum of 50 observations} \]
\[ \text{Sum of remaining 50 observations} = 800 - 500 = 300 \]

### Step 5: Calculate the mean of the remaining 50 observations
Now, we can find the mean of the remaining 50 observations using the sum we just calculated:
\[ \text{Mean of remaining 50 observations} = \frac{\text{Sum of remaining 50 observations}}{\text{Number of remaining observations}} \]
\[ \text{Mean of remaining 50 observations} = \frac{300}{50} = 6 \]

### Final Answer
The mean of the other 50 observations is **6**.

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