MathematicsFind the values of x   and y   if the median for the following data is 31.

Find the values of x   and y   if the median for the following data is 31.


  1. A
    10 and 8
  2. B
    8.5 and 10
  3. C
    8 and 10
  4. D
    8 and 10.5 

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    Solution:

    Given that the median of data is 31.
    Use formula
      Median=l+ N 2 −cf F h   .
    To find the values of x and y, write the table containing class intervals and calculate cumulative frequency.
    From the table it is clear that N = 40 and median is 31.
    Therefore the corresponding median class is 30-40. Here, l=30, f=y, cf=11+x, and h=10.
    Use formula Median=l+N2 - cff×h  to form equations in x and y.
    In the formula, l is the lower limit of the median class, N denotes the total number of observations, cf is the cumulative frequency of the preceding class, f is the frequency of each class and h is the class size.
    Median=l+N2 - cff×h  ⇒31=30+402 - 11 - xy×10  ⇒(31-30)y=(9-x)10
    ⇒y=90-10x
    ⇒y+10x=90             ……(1)
    Also the sum of frequency is 40.
    ⇒22+x+y=40
    ⇒x+y=40-22
    ⇒x+y=18       ……..(2)
    Subtract equation 2 from equation 1 and simplify.
    y+10x=90
    -y-x= -18
    ⇒9x=72
    ⇒x=8
    Substitute the value of x in equation 2 to calculate the value of y.
    8+y=18
    ⇒y=18-8
    ⇒y=10
    Therefore, the value of x = 8 and that of y = 10 .
    Hence, option 3 is correct.
     
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