Running total
Encyclopedia
A running total is the summation
of a sequence of numbers which is updated each time a new number is added to the sequence, simply by adding the value of the new number to the running total.
The purposes of a running total are twofold. First, it allows the total to be stated at any point in time without having to sum the entire sequence each time. Second, it can save having to record the sequence itself, if the particular numbers are not individually important.
Answer: 5 + 8 + 3 + 2 = 18. This is arrived at by simple summation of the sequence.
Now we insert the number 6 at the end of the sequence to get < 5 8 3 2 6 >. What is the total of that sequence?
Answer: 5 + 8 + 3 + 2 + 6 = 24. This is arrived at by simple summation of the sequence. But if we regarded 18 as the running total, we need only add 6 to 18 to get 24. So, 18 was, and 24 now is, the running total. In fact, we would not even need to know the sequence at all, but simply add 6 to 18 to get the new running total; as each new number is added, we get a new running total.
The same method will also work with subtraction, but in that case it is not strictly speaking a total (which implies summation) but a running difference; not to be confused with a delta. This is used, for example, when scoring the game of darts
. Similarly one can multiply instead of add to get the running product.
s display a running total of the purchases so far rung in. By the end of the transaction this will, of course, be the total of all the goods. Similarly, the machine may keep a running total of all transactions made, so that at any point in time the total can be checked against the amount in the till, even though the machine has no memory of past transactions.
Typically many games of all kinds use running totals for scoring; the actual values of past events in the sequence are not important, only the current score, that is to say, the running total.
The central processing unit
of computers for many years had a component called the accumulator
which, essentially, kept a running total (it "accumulated" the results of individual calculations). This term is largely obsolete with more modern computers. A betting accumulator is the running product of the outcomes of several bets in sequence.
Summation
Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed may be integers, rational numbers,...
of a sequence of numbers which is updated each time a new number is added to the sequence, simply by adding the value of the new number to the running total.
The purposes of a running total are twofold. First, it allows the total to be stated at any point in time without having to sum the entire sequence each time. Second, it can save having to record the sequence itself, if the particular numbers are not individually important.
Method
Consider the sequence < 5 8 3 2 >. What is the total of this sequence?Answer: 5 + 8 + 3 + 2 = 18. This is arrived at by simple summation of the sequence.
Now we insert the number 6 at the end of the sequence to get < 5 8 3 2 6 >. What is the total of that sequence?
Answer: 5 + 8 + 3 + 2 + 6 = 24. This is arrived at by simple summation of the sequence. But if we regarded 18 as the running total, we need only add 6 to 18 to get 24. So, 18 was, and 24 now is, the running total. In fact, we would not even need to know the sequence at all, but simply add 6 to 18 to get the new running total; as each new number is added, we get a new running total.
The same method will also work with subtraction, but in that case it is not strictly speaking a total (which implies summation) but a running difference; not to be confused with a delta. This is used, for example, when scoring the game of darts
Darts
Darts is a form of throwing game where darts are thrown at a circular target fixed to a wall. Though various boards and games have been used in the past, the term "darts" usually now refers to a standardised game involving a specific board design and set of rules...
. Similarly one can multiply instead of add to get the running product.
Use
While this concept is very simple, it is extremely common in everyday use. For example, most cash registerCash register
A cash register or till is a mechanical or electronic device for calculating and recording sales transactions, and an attached cash drawer for storing cash...
s display a running total of the purchases so far rung in. By the end of the transaction this will, of course, be the total of all the goods. Similarly, the machine may keep a running total of all transactions made, so that at any point in time the total can be checked against the amount in the till, even though the machine has no memory of past transactions.
Typically many games of all kinds use running totals for scoring; the actual values of past events in the sequence are not important, only the current score, that is to say, the running total.
The central processing unit
Central processing unit
The central processing unit is the portion of a computer system that carries out the instructions of a computer program, to perform the basic arithmetical, logical, and input/output operations of the system. The CPU plays a role somewhat analogous to the brain in the computer. The term has been in...
of computers for many years had a component called the accumulator
Accumulator (computing)
In a computer's central processing unit , an accumulator is a register in which intermediate arithmetic and logic results are stored. Without a register like an accumulator, it would be necessary to write the result of each calculation to main memory, perhaps only to be read right back again for...
which, essentially, kept a running total (it "accumulated" the results of individual calculations). This term is largely obsolete with more modern computers. A betting accumulator is the running product of the outcomes of several bets in sequence.