Let a, b, c, d, e, be the observations with mean m and standard deviation s. The standard deviation of the observations a+k, b+k, c+k, d+k, e+k is (a) `s` (b) `k s` (c) `s+k` (d) `s/k`

Options

A. s
B. ks
C. s+k
D. `s/k`

Explanation

To solve the problem, we need to find the standard deviation of the observations \( a+k, b+k, c+k, d+k, e+k \) given that the original observations \( a, b, c, d, e \) have a mean \( m \) and a standard deviation \( s \).

### Step-by-Step Solution:

1. **Understanding the Mean**:
The mean of the original observations \( a, b, c, d, e \) is given by:
\[ m = \frac{a + b + c + d + e}{5} \]
Therefore, we can express the sum of the observations as:
\[ a + b + c + d + e = 5m \]

2. **Calculating the New Mean**:
When we add \( k \) to each observation, the new observations become \( a+k, b+k, c+k, d+k, e+k \). The new mean \( m' \) is calculated as follows:
\[ m' = \frac{(a+k) + (b+k) + (c+k) + (d+k) + (e+k)}{5} = \frac{(a + b + c + d + e) + 5k}{5} \]
Substituting \( a + b + c + d + e = 5m \):
\[ m' = \frac{5m + 5k}{5} = m + k \]

3. **Understanding Standard Deviation**:
The standard deviation \( s \) is defined as:
\[ s = \sqrt{\frac{\sum (x_i - m)^2}{n}} \]
where \( n \) is the number of observations.

4. **Calculating the New Standard Deviation**:
The new observations \( a+k, b+k, c+k, d+k, e+k \) can be expressed in terms of the new mean \( m' \):
\[ s' = \sqrt{\frac{\sum ((x_i + k) - (m + k))^2}{5}} \]
Simplifying the expression:
\[ s' = \sqrt{\frac{\sum (x_i - m)^2}{5}} = s \]
This shows that adding a constant \( k \) to each observation does not affect the standard deviation.

5. **Conclusion**:
Therefore, the standard deviation of the new observations \( a+k, b+k, c+k, d+k, e+k \) remains the same as the original standard deviation \( s \).

### Final Answer:
The standard deviation of the observations \( a+k, b+k, c+k, d+k, e+k \) is \( s \).