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

Options

A. 45.5
B. 11.25, 1.25
C. 11.25.2.5
D. 12.5, 2.5

Answer

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

### Step 1: Understand the initial conditions
- The mean of the original observations (M) = 50
- The standard deviation of the original observations (SD) = 10
- The number of observations (N) = 100

### Step 2: Calculate the new mean
We need to subtract 5 from each observation and then divide the result by 4.

1. **Subtract 5 from the mean**:
\[ \text{New Mean} = M - 5 = 50 - 5 = 45 \]

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

### Step 3: Calculate the new standard deviation
The standard deviation is not affected by adding or subtracting a constant. However, it is affected by multiplication or division.

1. **Standard deviation remains the same after subtraction**:
\[ \text{New SD after subtraction} = SD = 10 \]

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

### Conclusion
- The new mean is **11.25**.
- The new standard deviation is **2.5**.

### Final Answer
The new mean and new standard deviation are **11.25 and 2.5** respectively.

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