The mean of a certain number of observations is 35. What is the new value of the mean if each observation is :
decreased by 5.

Answer

To find the new mean after each observation is decreased by 5, we can follow these steps:

### Step 1: Understand the given information
We know that the mean of a certain number of observations is 35. Let's denote the number of observations as \( n \).

### Step 2: Calculate the sum of the observations
The mean is defined as the sum of observations divided by the number of observations. Therefore, we can express the sum of the observations as:
\[ \text{Sum of observations} = \text{Mean} \times \text{Number of observations} = 35n \]

### Step 3: Adjust the observations
Since each observation is decreased by 5, the new sum of the observations can be calculated as follows:
\[ \text{New sum} = \text{Old sum} - \text{Total decrease} \]
The total decrease is \( 5 \) (the amount each observation is decreased) multiplied by \( n \) (the number of observations):
\[ \text{Total decrease} = 5n \]
Thus, the new sum becomes:
\[ \text{New sum} = 35n - 5n = 30n \]

### Step 4: Calculate the new mean
Now, we can find the new mean by dividing the new sum by the number of observations:
\[ \text{New mean} = \frac{\text{New sum}}{\text{Number of observations}} = \frac{30n}{n} = 30 \]

### Final Answer
The new mean after each observation is decreased by 5 is **30**.

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