the mean and standard deviation of two numbers are 22 and 4 respectively.find the numbers

Question

i want the answer of this question

Answer 1

Call the two numbers x and y.

 

Their mean is: (x + y) / 2 = 22

 

So, x + y = 44.

 

 

 

The numbers' standard deviation is harder to write an expression for. To find the standard deviation, you would first subtract each number from the mean and square each difference:

 

(22 - x)²

(22 - y)²

 

Then, find the mean of those values and take the square root:

 

√(((22 - x)² + (22 - y)²) / 2) = 4

((22 - x)² + (22 - y)²) / 2 = 16

(22 - x)² + (22 - y)² = 32

 

 

 

Now you have a system of equations:

 

x + y = 44

(22 - x)² + (22 - y)² = 32

 

Solve the first for x, then plug that into the second equation to solve for y:

 

x = 44 - y

 

(22 - (44 - y))² + (22 - y)² = 32

(y - 22)² + (22 - y)² = 32

y² - 44y + 484 + 484 - 44y + y² = 32

2y² - 88y + 968 = 32

y² - 44y + 484 = 16

y² - 44y + 468 = 0

(y - 26)(y - 18) = 0

 

y = 26 or y = 18

 

 

 

Notice that if y = 26 then x = 44 - 26 = 18 and if y = 18 then x = 44 - 18 = 26. So, the two numbers are 26 and 18.