Question

if xi is 3.2 ,5.8, 7.9, 4.5 and the fi are x, x+2 , x-3, x+6 respectively and the median is 4.876 find the value of x

Answer 1

arrange in assending order
xi fi cf
3.2 x x
4.5 x+6 2x+6
5.8 x+2 3x+8
7.9 x-3 4x+5
n/2th term= 4x+5/2
median =4.876
4x+5/2=4.876
4x+5=9.752
4x=4.752
x=1.188

Answer 2

Statistics :   Median..

Given data (ordered): Xi = 3.2,   4.5,    5.8,      7.9.
Their frequencies:        fi =   x,   x+6,    x-3,     x+2,   respectively.
Cumulative frequency: Fi =  x,  2x+6,  3x+3,  4x+5

So there are a total of 4x+5 data items in the given sample.

Middle of the sample:    (4x+5)/2 = 2 x + 2.5

So 2x+2.5 th data item is the median.  The data value Xi at position 2 x + 2.5,  is  4.5.

So the median is 4.5.

====
Probably there is a mistake in the question. The value given 4.876 is the arithmetic mean of the sample given. It is not the median.

So the Sum total of the data given:  

  Sum = 3.2 * x + 5.8 * (x+2) + 7.9 * (x-3) + 4.5 * (x+6)
           = 21.4 x + 14.9
  Number of data items in the sample:  4x + 5

Arith Mean = (21.4 x + 14.9) /(4x+5) = 4.876   given

    So 21.4 x + 14.9 = 19.504 x + 24.380
          x = 5
Answer... 5