To solve the problem, we'll calculate the following summations based on the provided dataTo solve the problem, we'll calculate the following summations based on the provided

Data Provided:

• Years:

  • 2018-2019
  • 2019-2020
  • 2020-2021
  • 2021-2022

• Degrees (X):

  • 1,308
  • 1,322
  • 1,425
  • 1,482

• Certificates (Y):

  • 840
  • 795
  • 889
  • 1,346

Required Summations:

1. ∑X: The sum of all Degrees (X).
2. ∑Y²: The sum of the squares of all Certificates (Y).
3. ∑XY: The sum of the products of Degrees (X) and Certificates (Y) for each year.
4. (∑Y)²: The square of the sum of all Certificates (Y).

Let's calculate each of these.

Calculations:

1. ∑X:

   • $∑X = 1308 + 1322 + 1425 + 1482$

2. ∑Y²:

   • $∑Y² = 840^2 + 795^2 + 889^2 + 1346^2$

3. ∑XY:

   • $∑XY = (1308 \times 840) + (1322 \times 795) + (1425 \times 889) + (1482 \times 1346)$

4. (∑Y)²:

   • $∑Y = 840 + 795 + 889 + 1346$
   • $(∑Y)² = (∑Y)^2$

I will calculate these values now.Here are the results of the calculations:

1. ∑X (Sum of Degrees): 5,537
2. ∑Y² (Sum of Squares of Certificates): 3,939,662
3. ∑XY (Sum of Products of Degrees and Certificates): 5,411,307
4. (∑Y)² (Square of the Sum of Certificates): 14,976,900

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. How do these summations relate to calculating correlation or regression?
2. What is the importance of summation notation in statistics?
3. How can we use these sums to calculate the mean of degrees and certificates awarded?
4. How would the result change if another year's data were added?
5. How can we interpret the squared sum of certificates in real-world scenarios?

Tip: Summation notation is a powerful tool in statistics and can be applied to various formulas, including those used in regression analysis and variance calculations. Understanding how to manipulate and interpret summation results is key to mastering these concepts.