If the mean of 25 obseviations is 27 and each observiations is decreased by 7 what will be the new mean ?

Options

A. 26.72
B. 27
C. 34
D. 20

Answer

To find the new mean after decreasing each observation by 7, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given data:**
- Number of observations (n) = 25
- Mean of the observations (M) = 27

2. **Calculate the total sum of the observations:**
- The mean is calculated as:
\[ \text{Mean} = \frac{\text{Sum of observations}}{n} \]
- Rearranging gives us:
\[ \text{Sum of observations} = \text{Mean} \times n = 27 \times 25 = 675 \]

3. **Determine the new sum after decreasing each observation by 7:**
- Since each observation is decreased by 7, the total decrease for all observations is:
\[ \text{Total decrease} = 7 \times n = 7 \times 25 = 175 \]
- Therefore, the new sum of the observations will be:
\[ \text{New sum} = \text{Old sum} - \text{Total decrease} = 675 - 175 = 500 \]

4. **Calculate the new mean:**
- The new mean can be calculated as:
\[ \text{New Mean} = \frac{\text{New sum}}{n} = \frac{500}{25} = 20 \]

### Final Answer:
The new mean after decreasing each observation by 7 is **20**.

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