The sum of 10 items is 12 and sum of their squares is 18, then find the standard deviation ?

Answer

To find the standard deviation given the sum of 10 items and the sum of their squares, we can follow these steps:

### Step 1: Identify the given values
- Number of items (n) = 10
- Sum of items (Σxi) = 12
- Sum of squares of items (Σxi²) = 18

### Step 2: Calculate the mean (μ)
The mean (μ) can be calculated using the formula:
\[ \mu = \frac{\Sigma xi}{n} \]
Substituting the values:
\[ \mu = \frac{12}{10} = 1.2 \]

### Step 3: Calculate the variance (σ²)
The variance (σ²) can be calculated using the formula:
\[ \sigma^2 = \frac{\Sigma xi^2}{n} - \left(\frac{\Sigma xi}{n}\right)^2 \]
Substituting the values:
\[ \sigma^2 = \frac{18}{10} - \left(\frac{12}{10}\right)^2 \]
Calculating each part:
\[ \sigma^2 = 1.8 - (1.2)^2 \]
\[ \sigma^2 = 1.8 - 1.44 \]
\[ \sigma^2 = 0.36 \]

### Step 4: Calculate the standard deviation (σ)
The standard deviation (σ) is the square root of the variance:
\[ \sigma = \sqrt{\sigma^2} = \sqrt{0.36} = 0.6 \]

### Final Answer
The standard deviation is **0.6**.

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