The mean of 100 observations is 40 and their standard deviation respectively is 10. if 5 is added to each observation then the new mean and new standard deviation will be

Options

A. 40,10
B. 40,15
C. 50,10
D. 45,10

Answer

To solve the problem step by step, we need to find the new mean and new standard deviation after adding 5 to each observation of the original data.

### Step 1: Understand the given data
We are given:
- Mean of 100 observations (x̄) = 40
- Standard deviation (σ) = 10
- Number of observations (n) = 100

### Step 2: Calculate the new mean
When we add a constant (in this case, 5) to each observation, the new mean (ȳ) can be calculated using the formula:
\[ ȳ = x̄ + k \]
where \( k \) is the constant added to each observation.

So, we have:
\[ ȳ = 40 + 5 = 45 \]

### Step 3: Calculate the new standard deviation
The standard deviation measures the spread of the data. When we add a constant to each observation, the standard deviation does not change. Therefore, the new standard deviation (σ_y) remains the same as the original standard deviation (σ_x).

So, we have:
\[ σ_y = σ_x = 10 \]

### Final Result
- New Mean = 45
- New Standard Deviation = 10