Mean of 9 observations in the data is 14. If each observation is multiplied by 4. then find the new mean is ____.

Answer

To solve the problem step by step, we need to find the new mean after multiplying each observation by 4.

### Step 1: Understand the given information
We know that the mean of 9 observations is 14.

### Step 2: Recall the formula for mean
The mean (average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]
In this case, we have:
\[ \text{Mean} = \frac{S}{9} = 14 \]
where \( S \) is the sum of the observations.

### Step 3: Calculate the sum of the observations
To find the sum \( S \), we can rearrange the formula:
\[ S = \text{Mean} \times \text{Total number of observations} = 14 \times 9 = 126 \]

### Step 4: Multiply each observation by 4
Now, if we multiply each observation by 4, the new sum of the observations becomes:
\[ \text{New Sum} = 4 \times S = 4 \times 126 = 504 \]

### Step 5: Calculate the new mean
The new mean can be calculated using the new sum and the same number of observations (which is still 9):
\[ \text{New Mean} = \frac{\text{New Sum}}{\text{Total number of observations}} = \frac{504}{9} = 56 \]

### Conclusion
Thus, the new mean after multiplying each observation by 4 is **56**.

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