SOLUTION: The following are the marks scored by 20 students in a test: 15 11 17 25 13 15 16 22 24 27 20 22 15 16 15 19 22 24 22 11 (a) Prepare a frequency table for th

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Question 1210334: The following are the marks scored by 20 students in a test:
15 11 17 25 13 15 16 22 24 27
20 22 15 16 15 19 22 24 22 11
(a) Prepare a frequency table for the distribution using class intervals 10 - 12, 13 - 15, 16-18....
(b) Calculate the variance of the distribution.
(c) If the pass mark for the test was 16, find the probability that a student selected at random from the class failed.
Answer by mccravyedwin(406) About Me  (Show Source):
You can put this solution on YOUR website!
class
interval  freq  midpoint(xi)   
  10-12     2       11
  13-15     5       14
  16-18     3       17
  19-21     2       20
  22-24     6       23
  25-27     2       26

mu%22%22=%22%22sum%28f%5Bi%5Dx%5Bi%5D%29%2Fsum%28f%5Bi%5D%29%22%22=%22%22%2811%2A2%2B14%2A5%2B17%2A3%2B20%2A2%2B23%2A6%2B26%2A2%29%2F%282%2B5%2B3%2B2%2B6%2B2%29%29%22%22=%22%22373%2F20%22%22=%22%2218.65  

We calculate the variance:

xi       xi-mu     (xi-mu)^2                fi(xi-mu)^2
-----------------------------------------------------------
11       -7.65      58.5225           2(58.5225) = 117.045   
14       -4.65      21.6225           5(21.6225) = 108.1125  
17       -1.65       2.7225            3(2.7225) =   8.1675 
20        1.35       1.9225            2(1.8225) =   3.645  
23        4.35      18.9225           6(18.9225) = 113.535  
26        7.35      54.0225           2(54.0225) = 108.045  
-----------------------------------------------------------
                                                   458.65

variance%22%22=%22%22sum%28f%5B1%5D%28x%5Bi%5D-mu%29%5E2%29%2Fsum%28f%5Bi%5D%29%22%22=%22%22458.65%2F20%22%22=%22%2222.9275

(c) 
2 were in 10-12 and 5 were in 13-15, so 2+5=7 failed
P(failure) = 7/20 = 0.35

Edwin