The mean of `8` numbers is `25.` If `5` is subtracted from each number, what will be the new mean ?

Options

A. `26`
B. `24`
C. `20`
D. `22`

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the sum of the original numbers
Given that the mean of 8 numbers is 25, we can find the sum of these numbers using the formula for mean:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Rearranging this gives us:
\[ \text{Sum of observations} = \text{Mean} \times \text{Number of observations} \]
Substituting the values:
\[ \text{Sum} = 25 \times 8 = 200 \]

### Step 2: Determine the effect of subtracting 5 from each number
If we subtract 5 from each of the 8 numbers, the total amount subtracted from the sum will be:
\[ \text{Total subtraction} = 5 \times 8 = 40 \]

### Step 3: Calculate the new sum
Now, we can find the new sum after subtracting 40 from the original sum:
\[ \text{New sum} = \text{Original sum} - \text{Total subtraction} = 200 - 40 = 160 \]

### Step 4: Calculate the new mean
Finally, we can find the new mean using the new sum and the same number of observations (which is still 8):
\[ \text{New Mean} = \frac{\text{New sum}}{\text{Number of observations}} = \frac{160}{8} = 20 \]

### Final Answer:
The new mean after subtracting 5 from each number is **20**.

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