Q - If we have the data (x, 22, 25, 30, y) in ascending order, the mean= 27and the range= 18 then the value of x=... and y=...?
Answers
Step-by-step explanation:
Given :-
The data x, 22, 25, 30, y are in the ascending order
Mean of the data =27
Range of the data = 18
To find :-
Find the values of x and y ?
Solution :-
Given observations are x, 22, 25, 30, y
Since they are in the ascending order
Lowest observation = x
Heighest observation = y
We know that
Range of the data = Heighest value-Lowest value
=>Range = y -x
According to the given problem
Range of the data = 18
Therefore, y-x = 18
=> y = x+18 ---------------(1)
and
Sum of all observations
= x+22+25+30+y
= 77+x+y
Number of all observations = 5
We know that
Mean = Sum of all observations/Number of all observations
=> Mean = (77+x+y)/5
According to the given problem
Mean = 27
=> (77+x+y)/5 = 27
=> 77+x+y = 27×5
=>77+x+y = 135
=> x+y = 135-77
=> x+y = 58-----------------(2)
On Substituting the value of y from (1) in (2)
=> x+x+18 = 58
=> 2x+18 = 58
=> 2x = 58-18
=> 2x = 40
=> x = 40/2
=> x = 20
On Substituting the value of x in (1)
=> y = 20+18
=> y = 38
Therefore, x = 20 and y = 38
Answer:-
The value of x = 20
The value of y = 38
Check:-
If x = 20 and y = 38 then
The observations = 20,22,25,30,38
They are ascending order
Range = Height value - Lowest value
=> R = 38-20
=> Range = 18
Mean = (20+22+25+30+38)/5
=> Mean = 135/5
=> Mean = 27
Verified the given relations in the given problem.
Used formulae:-
- Mean = Sum of all observations/Number of all observations
- Range of the data = Heighest value-Lowest value
Used Method:-
- Substitution method