Twenty students each score a mark of 20 out of a maximum of 40 marks in a test. What is the standard deviation of the scores for the twenty students? a. 2 b. 0 c. $$ 1 / 2 $$ d. 1

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Let the scores be denoted by $$ x_1, x_2, \dots, x_{20} $$ and each score is 20.

1. **Mean Calculation**:  
   The mean $$ \mu $$ is given by  
   $$
   \mu = \frac{1}{20} \sum_{i=1}^{20} x_i = \frac{1}{20} (20 + 20 + \cdots + 20) = 20.
   $$

2. **Variance Calculation**:  
   The variance $$ \sigma^2 $$ is given by  
   $$
   \sigma^2 = \frac{1}{20} \sum_{i=1}^{20} (x_i - \mu)^2.
   $$  
   Since $$ x_i = 20 $$ for all $$ i $$, we have  
   $$
   (x_i - 20)^2 = (20 - 20)^2 = 0.
   $$  
   Therefore,  
   $$
   \sigma^2 = \frac{1}{20} \cdot 20 \cdot 0 = 0.
   $$

3. **Standard Deviation Calculation**:  
   The standard deviation $$ \sigma $$ is the square root of the variance,  
   $$
   \sigma = \sqrt{\sigma^2} = \sqrt{0} = 0.
   $$

Thus, the standard deviation of the scores is 0. The correct answer is **(b) 0**.
The standard deviation of the scores is 0.

Twenty students each score a mark of 20 out of a maximum of 40 marks in a test. What is the standard deviation of the scores for the twenty students? a. 2 b. 0 c. \( 1 / 2 \) d. 1

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