If for a sample of size 60, we have the following information `sumxi^2=18000a n dsumxi=960` , then the variance is
a)6.63
(b) 16
(c) 22
(d) 44

Options

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

Explanation

To find the variance of the given sample, we can use the formula for variance:

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

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

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

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

\[ \frac{\sum x_i^2}{n} = \frac{18000}{60} = 300 \]

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

\[ \frac{\sum x_i}{n} = \frac{960}{60} = 16 \]

### Step 3: Calculate \(\left(\frac{\sum x_i}{n}\right)^2\)

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

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

\[ \sigma^2 = 300 - 256 \]

### Step 5: Calculate the variance

\[ \sigma^2 = 44 \]

Thus, the variance is \(44\).

### Conclusion

The correct answer is (d) 44.

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