What is the difference between sum and cumulative sum?
The Correct Answer and Explanation is :
The terms “sum” and “cumulative sum” refer to two related but distinct concepts in mathematics and data analysis.
Sum is a basic arithmetic operation that refers to the total value obtained by adding two or more numbers together. For instance, if you have a set of numbers, say ( a = [2, 3, 5] ), the sum would be calculated as ( 2 + 3 + 5 = 10 ). The sum provides a single value representing the total of the numbers in the set.
On the other hand, cumulative sum (often abbreviated as CUMSUM) is a sequence of partial sums of a given data set. Essentially, the cumulative sum at each point in the sequence is the sum of all the previous numbers up to that point, including the current number. Using the previous example, the cumulative sum of ( a = [2, 3, 5] ) would be:
- Cumulative sum at index 0: ( 2 )
- Cumulative sum at index 1: ( 2 + 3 = 5 )
- Cumulative sum at index 2: ( 2 + 3 + 5 = 10 )
So the cumulative sums would be ( [2, 5, 10] ).
In practical applications, cumulative sums are useful in various fields such as finance, statistics, and computer science. They help track changes over time, making them ideal for analyzing trends in data. For example, in a financial context, a cumulative sum could represent the running total of daily sales over a month, allowing businesses to assess performance and make informed decisions.
In summary, the key difference between sum and cumulative sum is that the sum yields a single total value, while the cumulative sum provides a running total that reflects the progression of sums through a sequence of numbers.