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Easy

Question

The frequency distribution of the marks obtained by 100 students in a test carrying 50 marks is given below Then the mean is

  1. 28.3    
  2. 28    
  3. 27.3    
  4. 26.4    

hintHint:

The direct method is the simplest method to find the mean of the grouped data. The steps that can be followed to find the mean for grouped data using the direct method are given below,
  • Create a table containing four columns as given below,
    Column 1- Class interval.
    Column 2- Class marks (corresponding), denoted by xiblank i.
    Column 3- Frequencies (f subscript i) (corresponding)
    Column 4- x subscript i f subscript i (corresponding product of column 2 and column 3)
  • Calculate Mean by the Formula Mean = ∑x subscript i f subscript i/∑f subscript i

The correct answer is: 28.3


     Given :
    The frequency distribution of the marks obtained by 100 students in a test carrying 50 marks is given below

    Step 1 : Create a table containing four columns as given below,

    Class interval x subscript i f subscript i x subscript i f subscript i
    0-9 fraction numerator 0 plus 9 over denominator 2 end fraction space equals 4.5 8 36
    10-19 fraction numerator 10 plus 19 over denominator 2 end fraction space equals 14.5 15 217.5
    20-29 fraction numerator 20 plus 29 over denominator 2 end fraction space equals 24.5 20 490
    30-39 fraction numerator 30 plus 39 over denominator 2 end fraction space equals 34.5 45 1552.5
    40-49 fraction numerator 40 plus 49 over denominator 2 end fraction space equals 44.5 12 534
        begin inline style stack sum f subscript i space equals space 100 with blank below end style begin inline style sum for blank of end style x subscript i f subscript i space end subscript space equals space 2830

    M e a n space equals space fraction numerator stack sum f subscript i x subscript i with blank below over denominator stack sum f subscript i with blank below end fraction space equals space 2830 over 100 space equals space 28.3

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