Estimated and projected enrollments in two-year colleges for 2016, 2020, and 2024 are shown in the table. Estimate enrollments for 2018 & 2022

Question

Midpoint formula:

• M=(x₁+x₂/2) , (y₂+y₁/2)

 

Year.     Enrollments(in millions)

2016.       7.1

2020.       7.8

2024.       8.0

 

Answer 1

The midpoint formula is M=(x₁+x₂)/2 , (y₁+y₂)/2  Placement of the parenthesis is extremely important; putting the parenthesis around the values indicates the values are added first, then divided by two.

 

You can estimate the value between two points by using the midpoint (average) of the two numbers.  

 

For example, if enrollment in 2016 is 7.1 million, and enrollment in 2020 is 7.8 million, we can estimate the enrollment in 2018 (midway between those two years) by finding the midpoint of 2016 enrollment and 2020 enrollment.

 

Using the formula, the midpoint between two values is (y₁+y₂)/2.

 

The midpoint between 2016's enrollment (7.1 million) and 2020's enrollment (7.8 million) is 7.45 million ( (7.1+7.8)/2 ).

 

To do this graphically, we could assign the year as the x-value, and the enrollment as the y-value.

X₁ = 2016      Y₁= 7.1
X₂ = 2020      Y₂ = 7.8
X₃ = 2024      Y₃ = 8.0

 

The midpoint of points 1 and 2, using the formula, would be (2018, 7.45)

          M = (x₁+x₂)/2 , (y₁+y₂)/2

          M = (2016+2020)/2 , (7.1+7.8)/2

          M = 2018, 7.45     this states that in year 2018, the enrollment is estimated to be 7.45 million.