if the median of 6,7,x-2,x,17 and 20 written in ascending order is 16 . find the volume of x
Answers
Answer:
ANSWER
Given if the observations of 6,7,x−2,x,17,20 are written in ascending order and their median is 16
6,7,x−2,x,17,20
Here observe that no of observations six i.e even
So median is average of
2
n
th
term & (
2
n
+1)
th
term
Median =
2
2
n
th
term+(
2
n
+1)
th
term
=
2
2
6
th
term+(
2
6
+1)
th
term
16=
2
3
th
term+4
th
term
16=
2
x−2+x
=
2
2x−2
=
2
2(x−1)
16=x−1
x=16+1
Value of x=17
∴6,7,17−2,17,17,20
6,7,15,17,17,20
mean=
No of observations
sum of observations
=
6
6+7+15+17+17+20
mean =
6
82
=13.67
there is the answer dear
SOLUTION :
The correct option is (c): 17
Given : Median = 16 , observations are = arrange in ascending order :6, 7, x - 2, x, 17, 20
Total number of observations = 6
n = 6 (even)
If n is even then median = 12value of [ (n/2)th + (n/2 +1) th] observations.
Median = 1/2[(6/2)th + (6/2 + 1) th] observations
Median = 2 [3th + 4th] observations
16 = 2 [(x - 2) + X
16 x 2 = 2x - 2
2x = 32 + 2
2x = 34
X - 34/2 = 17 =
x = 17
Hence, the value of x is 17.
** Median of the data depends on the number of observations (n).
i) If n is odd then median= value of [(n+1)/ 2]th observation
ii) If n is even then median= value of [ (n/2)th + (n/2 +1) th] observations.
HOPE THIS ANSWER WILL HELP YOU......