The mean of 100 observation is 50 and the standard deviation is 10. If 5 is subtracted from each observation and then it is divided by 4, then what will be the new mean and the new standard respectively?

Options

A. 45, 5
B. 11.25, 1.25
C. 11.25, 2.5
D. 12.5. 2.5

Explanation

To solve the problem step by step, we will find the new mean and new standard deviation after performing the specified operations on the original observations.

### Given:
- Mean (x̄) = 50
- Standard Deviation (σ) = 10
- Number of Observations (n) = 100

### Step 1: Calculate the new mean
1. **Subtract 5 from each observation**:
The new mean after subtracting 5 from each observation can be calculated as:
\[ \text{New Mean} = \text{Old Mean} - 5 = 50 - 5 = 45 \]

2. **Divide the result by 4**:
Now, divide the new mean by 4:
\[ \text{New Mean} = \frac{45}{4} = 11.25 \]

### Step 2: Calculate the new standard deviation
1. **Standard deviation is not affected by constant subtraction**:
The standard deviation remains the same when we subtract a constant from each observation. Thus, after subtracting 5, the standard deviation is still:
\[ \sigma' = 10 \]

2. **Divide the standard deviation by 4**:
Now, we divide the standard deviation by 4:
\[ \text{New Standard Deviation} = \frac{10}{4} = 2.5 \]

### Final Answers:
- New Mean = 11.25
- New Standard Deviation = 2.5