Question

the number 2,3,4,4,3x-1,3x+1,7,7,8 are written in ascending order . if the median is 5 find x.hence find mode

Answer 1

Hi there !!!

Here ,
No: of observations = n = 9 [ even ]

AS the number of observations is even ,

Median = $\frac{n +1}{2}$
          
            = $\frac{9+1}{2}$
              
            = $\frac{10}{2}$
  
            = 5 th observation

Median = 5 th observation =  3x - 1

We are given that median = 5

so , 


3x - 1 = 5

3 x = 5+1

3x = 6

x  =  $\frac{6}{3}$

x = 2

So the numbers are :

3x - 1 = 3 ×2 - 1 = 5

3x + 1 = 3 × 2 + 1 = 7


2 , 3 , 4 , 4 ,  5 , 7 , 7 , 7 ,8

Mode is the frequently occurring number.

Here , the frequently occurring number is 7

Hence ,
mode = 7

Answer 2

here no of observations=9.

n=9

9 is odd .

we know that if n is odd , then 

median = (n+1)/2

             =(9+1)/2 

              =10/2

             =5th term

 
 in the given observations, 5th term is 3x-1.

given that median is 5.

so, 3x-1=5.
       
     3x=5+1
   
     3x=6
  
     x=6/3

      x=2.

so the value of x = 2.

3x-1=3*2-1

       =5

3x+1=3*2+1

        =6+1

        =7

the given observations are 2,3,4,4,5,7,7,7,8.

in these observations 7 occurred most frequently.

hence mode is 7.

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