Question

Calculate standard deviation and coefficient from the following information. use direct method. (5marks) marks obtained by 5students are given as : 10, 8, 6, 14 and 12.​

Answer 1

Answer:

data is 20 and coefficient of Range (CR) is 0.4

Answer 2

Answer:

Standard deviation = 2$\sqrt{2}$  and coefficient of variation =28.28%  

Explanation:

Given data

Marks obtained by 5 students are  10, 8, 6, 14, 12

here we need to find standard deviation and coefficient  

the formula for standard deviation for ungrouped data in direct method  is given by    √ ∑$x_{i}^{2}$/n - (x)²

here n = number of values in given data = 5

        we need to find ∑$x_{i} ^{2}$ values  

⇒ mean of given data = sum of the observations/ n  

                                   $x$ = $\frac{10+8+6+14+12}{5}$ =  $\frac{50}{5}$ = 10

          $x_{i}$       10        8        6      14       12  

          $x_{ i} ^{2}$      100      64      36    196     144            

⇒   ∑$x_{i}^{2}$  = 540    , n = 5    , x = 10

⇒ standard deviation  SD = $\sqrt{\frac{540 }{5} - 100 }$

                                            = $\sqrt{108-100}$    

                                            = $\sqrt{8}$ = $\sqrt{4(2)}$ = 2$\sqrt{2}$  

⇒ coefficient of variation = $\frac{SD}{mean} (100)$  [SD = standard deviation]

                                          = $\frac{2\sqrt{2} }{10} (100)$

                                          = 2$\sqrt{2}$ (10)   [ $\sqrt{2}$ taken as 1.414 ]

                                          = 2(1.414)10 = 28.28 %