Find x and y so that the ordered data set as a mean of 42and a median of 35.
17,22,26,29,34,x,42,67,70,56,y
soln:
17+22+26+29+34+x+42+67+70+56+y= 363+x+y
(363+x+y)/11=42
y=99/x
x is median
this is not the right ans or u have fully done it
67
Lolkhljohihhh
To find x and y such that the ordered data set has a mean of 42 and a median of 35, we can follow these steps:
Step 1: Find the sum of all the values in the data set and set it equal to the sum of the data set multiplied by the number of elements.
The sum of the values is calculated as follows:
17 + 22 + 26 + 29 + 34 + x + 42 + 67 + 70 + 56 + y = 363 + x + y.
Step 2: Express the mean by dividing the sum obtained in Step 1 by the number of elements in the data set.
The mean is given as 42. So, we can set up the equation:
(363 + x + y) / 11 = 42.
Step 3: Solve the equation obtained in Step 2 to find the values of x and y.
To solve this equation for x and y, we need an additional equation relating them.
Step 4: Use the fact that the median is 35 to find the relationship between x and y.
Since x is the median, it falls in the middle of the ordered data set. To maintain a median of 35, y must be the same as x, as they will both be greater than 35.
So, we can set up the equation: y = 99/x.
Step 5: Substitute the relationship obtained in Step 4 into the equation from Step 2.
Substituting y = 99/x into the equation (363 + x + y) / 11 = 42 gives us:
(363 + x + 99/x) / 11 = 42.
Step 6: Solve the equation obtained in Step 5 to find the value of x.
To solve this equation, we can multiply both sides by 11 to eliminate the denominator:
363 + x + 99/x = 11 * 42.
Simplifying, we have:
363 + x + 99/x = 462.
Multiplying throughout by x gives us:
363x + x^2 + 99 = 462x.
Rearranging the equation gives us a quadratic equation:
x^2 - 99x + 99 = 0.
Step 7: Solve the quadratic equation obtained in Step 6 to find the value of x.
We can solve this quadratic equation using factoring, completing the square, or using the quadratic formula.
The solutions for x are:
x = 3 and x = 33.
Therefore, x can be either 3 or 33.
Step 8: Substitute the value of x obtained in Step 7 into the equation from Step 4 to find the value of y.
Using the equation y = 99/x, we can substitute x = 3 and x = 33:
For x = 3, y = 99/3 = 33.
For x = 33, y = 99/33 = 3.
Therefore, when x = 3, y = 33, and when x = 33, y = 3.
Hence, the pairs (x, y) that satisfy the given conditions are (3, 33) and (33, 3).
17+22+26+29+34+x+42+67+70+56+y= 363+x+y/11=42
X=36
Y=70
17+22+26+29+34+x+42+67+70+56+y= 363+x+y/11=42
y=99/x=67