MathematicsThe arithmetic mean of the following frequency distribution is 56. Determine the value of p  .Class intervalFrequencies(fi)Mid-value(xi)fi xi0-20161016020-40113033040-602550125060-80P7070p80-10012901080100-120101101100Total74+p 3920+70p

The arithmetic mean of the following frequency distribution is 56. Determine the value of p  .


Class interval

Frequencies(fi)

Mid-value(xi)

fi xi

0-20

16

10

160

20-40

11

30

330

40-60

25

50

1250

60-80

P

70

70p

80-100

12

90

1080

100-120

10

110

1100

Total

74+p

 

3920+70p


  1. A
    10
  2. B
    15
  3. C
    12
  4. D
    16 

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    Solution:

    Given, mean is 56.

    Class interval

    Frequencies(fi)

    Mid-value(xi)

    fi xi

    0-20

    16

    10

    160

    20-40

    11

    30

    330

    40-60

    25

    50

    1250

    60-80

    P

    70

    70p

    80-100

    12

    90

    1080

    100-120

    10

    110

    1100

    Total

    74+p

     

    3920+70p

    We know that,
    Mean = f i x i f i = 3920+70p 74+p  
    Since mean is 56,
    3920+70p 74+p =56   3920+70p 74+p =56 3920+70p=56×(74+p) 3920+70p=4144+56p 70p56p=41443920 14p=224 p= 224 14 p=16  
    Thus, p = 16.
    Therefore, the correct option is 4.
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