Question

if the median of data 7, 10, 12 ,p, q,27 ,31 is 17 .if one additional term 40 is added new median is 18 find p and q​

Answer 1

Step-by-step explanation:

Given- median of data-> 7,10,12,p,q,27,31 is 17

Since the number of terms are odd,therefore median = (n+1/2)^th term where n=total no. of terms

Here,total no. of terms=7

=> median = (7+1/2)^th term = 17

=( 8/2)^th term = 17

= 4^th term = 17

Here,4^th term = p

=> p = 17

It is given that when we add an additional term

i. e. 40,median becomes 18

Now,the total number of terms are even i.e.= 8 terms,therefore median =[(n/2)^th term + (n/2 +1)^th term]/2

Here,n = total number of terms = 8 terms

=> median=[(8/2)^th term + (8/2+1)^th term]/2 = 18

= ( 4^th term + 5^th term)/2 =18

Here,4^th term=p ,5^th term =q

=> median = p+q/2=18 = p+q=36

put value of p from above,

=> 17 + q =36

=>q = 19

Therefore,p=17,q=19 ans.