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Wikipedia

Running total

A running total or rolling total is the summation of a sequence of numbers which is updated each time a new number is added to the sequence, by adding the value of the new number to the previous running total. Another term for it is partial sum.

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. 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 registers 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.

See also

running, total, this, article, does, cite, sources, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor, june, 2019, learn, when, remove, t. This article does not cite any sources Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Running total news newspapers books scholar JSTOR June 2019 Learn how and when to remove this template message A running total or rolling total is the summation of a sequence of numbers which is updated each time a new number is added to the sequence by adding the value of the new number to the previous running total Another term for it is partial sum 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 EditConsider the sequence lt 5 8 3 2 gt 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 lt 5 8 3 2 6 gt 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 Use EditWhile this concept is very simple it is extremely common in everyday use For example most cash registers 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 See also EditRunning average Prefix sum Retrieved from https en wikipedia org w index php title Running total amp oldid 1134644811, wikipedia, wiki, book, books, library,

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