If for a sample of size 60, we have the following information `sum(x_(i))^2=18000` and `sumx_(i)=960` , then the variance is

Options

A. 6.63
B. 16
C. 22
D. 44

Explanation

To find the variance of the given sample, we will use the formula for variance in the context of a sample:

\[ \text{Variance} (s^2) = \frac{\sum x_i^2}{n} - \left(\frac{\sum x_i}{n}\right)^2 \]

Where:
- \(\sum x_i^2\) is the sum of the squares of the observations.
- \(\sum x_i\) is the sum of the observations.
- \(n\) is the sample size.

Given:
- \(\sum x_i^2 = 18000\)
- \(\sum x_i = 960\)
- \(n = 60\)

### Step 1: Calculate \(\frac{\sum x_i^2}{n}\)

\[ \frac{\sum x_i^2}{n} = \frac{18000}{60} \]

Calculating this gives:

\[ \frac{18000}{60} = 300 \]

### Step 2: Calculate \(\frac{\sum x_i}{n}\)

\[ \frac{\sum x_i}{n} = \frac{960}{60} \]

Calculating this gives:

\[ \frac{960}{60} = 16 \]

### Step 3: Square the result from Step 2

Now we need to square the result from Step 2:

\[ \left(\frac{\sum x_i}{n}\right)^2 = 16^2 = 256 \]

### Step 4: Substitute values into the variance formula

Now we can substitute the values into the variance formula:

\[ \text{Variance} (s^2) = 300 - 256 \]

Calculating this gives:

\[ s^2 = 44 \]

### Final Answer

Thus, the variance of the sample is:

\[ \text{Variance} = 44 \]

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