If `n= 10, sum_(i=1)^(10) x_(i) = 60` and `sum_(i=1)^(10) x_(i)^(2) = 1000` then find s.d.

Answer

To find the standard deviation (s.d.) given the values, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- \( n = 10 \)
- \( \sum_{i=1}^{10} x_i = 60 \)
- \( \sum_{i=1}^{10} x_i^2 = 1000 \)

2. **Use the formula for standard deviation:**
The formula for the standard deviation is:
\[ s.d. = \sqrt{\frac{\sum_{i=1}^{n} x_i^2}{n} - \left(\frac{\sum_{i=1}^{n} x_i}{n}\right)^2} \]

3. **Calculate \( \frac{\sum_{i=1}^{10} x_i^2}{n} \):**
\[ \frac{\sum_{i=1}^{10} x_i^2}{n} = \frac{1000}{10} = 100 \]

4. **Calculate \( \frac{\sum_{i=1}^{10} x_i}{n} \):**
\[ \frac{\sum_{i=1}^{10} x_i}{n} = \frac{60}{10} = 6 \]

5. **Square the result from step 4:**
\[ \left(\frac{\sum_{i=1}^{10} x_i}{n}\right)^2 = 6^2 = 36 \]

6. **Substitute the results into the standard deviation formula:**
\[ s.d. = \sqrt{100 - 36} \]

7. **Calculate the difference:**
\[ 100 - 36 = 64 \]

8. **Take the square root:**
\[ s.d. = \sqrt{64} = 8 \]

### Final Answer:
The standard deviation (s.d.) is \( 8 \).