The mean of 20 numbers is 43. if 6 is subtracted from each of the numbes what will be the new mean ?

Answer

To find the new mean after subtracting 6 from each of the 20 numbers, we can follow these steps:

### Step 1: Calculate the total sum of the original numbers.
The mean of a set of numbers is calculated as the total sum of the numbers divided by the count of the numbers.

Given:
- Mean = 43
- Number of values (n) = 20

Using the formula for mean:
\[ \text{Mean} = \frac{\text{Total Sum}}{n} \]
We can rearrange this to find the total sum:
\[ \text{Total Sum} = \text{Mean} \times n = 43 \times 20 = 860 \]

### Step 2: Subtract 6 from each number.
If we subtract 6 from each of the 20 numbers, the total amount subtracted from the sum will be:
\[ \text{Total Subtraction} = 6 \times 20 = 120 \]

### Step 3: Calculate the new total sum.
Now, we subtract the total amount subtracted from the original total sum:
\[ \text{New Total Sum} = \text{Original Total Sum} - \text{Total Subtraction} = 860 - 120 = 740 \]

### Step 4: Calculate the new mean.
The new mean can be calculated using the new total sum and the same number of values (20):
\[ \text{New Mean} = \frac{\text{New Total Sum}}{n} = \frac{740}{20} = 37 \]

### Final Answer:
The new mean after subtracting 6 from each of the numbers is **37**.

---