Question

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=...?

Answer 1

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