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General Mathematics Paper 2, Nov/Dec. 2009  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 Main
General Comments
Weakness/Remedies
Strength
Question 7

The marks scored by 50 students in a Geography examination are as follows:
           
            60        54        40        67        53        73        37        55        62        43
            44        69        39        32        45        58        48        67        39        51
            46        59        40        52        61        48        23        60        59        47
            65        58        74        47        40        59        68        51        50        50
            71        51        26        36        38        70        46        40        51        42

  1. Using a class interval of 21-30, 31-40, …, prepare a frequency distribution table.
  2. Draw a histogram to represent the distribution.
  3. Use your histogram to estimate the modal mark.
  4. If a student is selected at random, find the probability that he/she obtains a mark greater than 63.
_____________________________________________________________________________________________________
Observation

This was also another question which was reportedly attempted by majority of the candidates and their performance was described as fair.  It was also reported that many candidates drew bar charts instead of histograms while others did not use class boundaries in drawing the graph but they rather used class limits.  Interpretation of the graph was also an observed challenge.

The grouped frequency table is given by
   Class        f        Cf       Class
  Interval                         Boundary
 

    21-30     2        2        20.5 - 30.5  
                31-40    10      12       30.5 - 40.5
                41-50    12      24       40.5 - 50.5
                51-60    15      39       50.5 - 60.5
                61-70      8      47       60.5 - 70.5
                71-80      3      50       70.5 - 80.5
 

               The graph is given below

 

 

 

 

 

 

 

The modal mark derived from the graph = 53 while the probability = no. of candidates who scored marks greater than 63 ÷ total number of students             i.e. 9/50 = 0.18.
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