What is the standard deviation ?
For the next two (02) items that follow : The frequency distribution of marks obtained by 100 students in a certain subject is given below : <table border='1' cellpadding='6' cellspacing='0'> <tr><th>Marks</th><th>0-10</th><th>10-20</th><th>20-30</th><th>30-40</th></tr> <tr><td>No. of students</td><td>10</td><td>20</td><td>f</td><td>40</td></tr> </table>
- A. 8.5
- B. 9
- C. 9.5
- D. 10 ✓
Correct Answer: D. 10
Explanation
Variance = \sum f_i(x_i - \text{mean})^2 / 100 = (10*20^2 + 20*10^2 + 30*0^2 + 40*10^2)/100 = (4000 + 2000 + 0 + 4000)/100 = 100. Standard Deviation = \sqrt{100} = 10.
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