The arithmetic mean of a set of 40 values is 65. If the 40 values is increased by 5, then the mean of the new set of values is

Options

A. 65
B. 70
C. 60
D. cannot be deterimed

Answer

To solve the problem step-by-step, we will follow the given information and apply the formula for the arithmetic mean.

### Step 1: Understand the given information
We know that the arithmetic mean (AM) of a set of 40 values is 65. This means:
\[ \text{AM} = \frac{\text{Sum of all values}}{\text{Number of values}} \]

### Step 2: Calculate the sum of the original values
Let the sum of the 40 values be \( S \). According to the formula for the arithmetic mean:
\[ 65 = \frac{S}{40} \]
To find \( S \), we can rearrange this equation:
\[ S = 65 \times 40 \]
Calculating this gives:
\[ S = 2600 \]

### Step 3: Increase each value by 5
Now, if each of the 40 values is increased by 5, the new values will be:
\[ N_1 + 5, N_2 + 5, N_3 + 5, \ldots, N_{40} + 5 \]
The new sum of these values will be:
\[ S' = (N_1 + 5) + (N_2 + 5) + (N_3 + 5) + \ldots + (N_{40} + 5) \]
This can be simplified to:
\[ S' = (N_1 + N_2 + N_3 + \ldots + N_{40}) + 40 \times 5 \]
Substituting \( S \) into this equation:
\[ S' = 2600 + 200 = 2800 \]

### Step 4: Calculate the new arithmetic mean
Now, we can find the new arithmetic mean \( AM' \):
\[ AM' = \frac{S'}{40} = \frac{2800}{40} \]
Calculating this gives:
\[ AM' = 70 \]

### Conclusion
The new arithmetic mean of the set of values after increasing each by 5 is **70**.