For a series the information available is `n = 10 sum x = 60, sum x^(2) = 1000`. The standard deviation is

Options

A. 8
B. 64
C. 24
D. 128

Answer

To find the standard deviation for the given series, we will follow these steps:

### Step 1: Write down the given information.
We have:
- \( n = 10 \) (the number of observations)
- \( \sum x = 60 \) (the sum of the observations)
- \( \sum x^2 = 1000 \) (the sum of the squares of the observations)

### Step 2: Use the formula for standard deviation.
The formula for the standard deviation \( \sigma \) is given by:

\[ \sigma = \sqrt{\frac{\sum x^2}{n} - \left(\frac{\sum x}{n}\right)^2} \]

### Step 3: Substitute the values into the formula.
Now, we can substitute the values we have into the formula:

\[ \sigma = \sqrt{\frac{1000}{10} - \left(\frac{60}{10}\right)^2} \]

### Step 4: Simplify the expression.
Calculating each term:

1. Calculate \( \frac{1000}{10} \):
\[ \frac{1000}{10} = 100 \]

2. Calculate \( \frac{60}{10} \):
\[ \frac{60}{10} = 6 \]

3. Now, calculate \( \left(\frac{60}{10}\right)^2 \):
\[ 6^2 = 36 \]

### Step 5: Substitute back into the formula.
Now we substitute these values back into the formula:

\[ \sigma = \sqrt{100 - 36} \]

### Step 6: Calculate the final value.
Now, calculate \( 100 - 36 \):
\[ 100 - 36 = 64 \]

So, we have:
\[ \sigma = \sqrt{64} \]

Finally, calculate the square root:
\[ \sigma = 8 \]

### Conclusion:
The standard deviation is \( 8 \).