IQR = 40
1) Put the numbers in order: 40, 45, 50, 60, 60, 75, 90, 90, 120
2) Find the median: Median is 60 (the 2nd one)
3) Place parentheses around the numbers above and below the median. For easy identification of Q1 and Q3. (40, 45, 50, 60,) 60, (75, 90, 90, 120)
4) Find the Q1 and Q3. Q1 = median of the lower half of the data; Q3 = median of the higher half of the data. Q1 and Q3 have even sets so its median cannot be defined.
5) Had both sets contain odd sets, the median of Q1 is subtracted from the median of Q3 to get the IQR.
We can then use the Alternative definition of IQR.
IQR is the difference between the largest and smallest values in the middle 50% of a set data.
40, 45, 50, 60, 60, 75, 90, 90, 120
Middle 50% is 50, 60, 60, 75, 90; IQR = Largest value - smallest value;
IQR = 90 - 50 = 40
Answer:
D
If you put the equation into a calculator, it will show a graph of it.
Let, the age of Daniel be x years and Kevin be y years.
Given, Kevin is 3 years older than Daniel.
So we can write the equation as y=x+3
Also given, 2 years ago Kevin was 4 times as old as Daniel.
2 years ago, Daniel's age = (x-2) years
2 years ago, Kevin's age = (y-2) years.
So we can write the equation as (y-2) = 4(x-2)
We have got the two equations
y = x+3 ..... equation 1
(y-2) = 4(x-2) ..... equation 2
Now we are plugging in the value of y from equation 1 to equation 2
x+3-2 = 4(x-2)
x+1 = 4(x-2)
Now we have to distribute 4 in the right side.
x+1 = 4x -8
We will have to take x in one side. so let's move 4x to the left side by subtracting it to both sides.
x -4x+1 = 4x-4x -8
-3x+1 = 0-8
-3x+1 = -8
Now we have to move 1 to the right side by subtracting 1 from both sides.
-3x +1 -1 = -8-1
-3x+0 = -9
-3x = -9
Now we can get x by moving -3 to the right side. As -3 is multiplied there so we can move it by dividing both sides by -3.
-3x/-3 = -9/-3
x = 3
So we have got the required answer. Daniel is 3 years old.
