# How do you find the AVERAGE of numbers on a Mac?

Basic modelEditNumbers works in a fashion somewhat different from traditional spreadsheets like Microsoft Excel or Lotus 1-2-3. In the traditional model, the table is the first-cla

### Basic modelEdit

Numbers works in a fashion somewhat different from traditional spreadsheets like Microsoft Excel or Lotus 1-2-3. In the traditional model, the table is the first-class citizen of the system, acting as both the primary interface for work and as the container for other types of media like charts or digital images. In effect, the spreadsheet and the table are the same. In contrast, Numbers uses a separate "canvas" as its basic container object and tables are among the many objects that can be placed within the canvas.[6][N 1]

This difference is not simply a case of syntax. To provide a large workspace, conventional spreadsheets extend a table in X and Y to form a very large grid ideally infinite, but normally limited to some smaller dimension. [N 2] Some of these cells, selected by the user, hold data. Data is manipulated using formulas, which are placed in other cells in the same sheet and output their results back into the formula cell's display. The rest of the sheet is "sparse", currently unused.[8]

Sheets often grow very complex with input data, intermediate values from formulas, and output areas, separated by blank areas. To manage this complexity, Excel allows one to hide data that is not of interest,[9] often intermediate values. Quattro Pro commonly introduced the idea of multiple sheets in a single book, allowing further subdivision of the data; Excel implements this as a set of tabs along the bottom of the workbook.

In contrast, Numbers does not have an underlying spreadsheet in the traditional sense but uses multiple individual tables for this purpose.[6] Tables are an X and Y collection of cells, like a sheet, but extend only to the limits of the data they hold. Each section of data or output from formulas can be combined into an existing table or placed into a new table. Tables can be collected by the user onto single or multiple canvases. Whereas a typical Excel sheet has data strewn across it, a Numbers canvas could build the same output through smaller individual tables encompassing the same data.[10]

### Formulas and functionsEdit

A newly created Numbers document is styled to indicate suggested header areas in column A and row 1. Note that the table stops in the lower right of the screen, which can be resized with the widget in the corner.

After adding data and headers, Numbers has automatically created named ranges over the data. The ranges were used to create a formula that has populated column D. Note that the same formula can be used for the entire column the row number is not required.

The table has been resized to show only the used area, moved into the center of the canvas, and styled. A chart has been added above the table. The pane in the upper left shows an object tree, with the "canvas" objects being shown in a hierarchy of each sheet, every sheet can be collapsed or expanded to show the canvas object contained within that sheet.

Consider a simple spreadsheet used to calculate the average value of all car sales in a month for a given year. The sheet might contain the month number or name in column A, the number of cars sold in column B, and the total income in column C. The user wishes to complete the task of "calculating the average income per car sold by dividing the total income by the number of cars sold and putting the resulting average in column D". From the user's perspective, the values in the cells have semantic content, they are "cars sold" and "total income" and they want to manipulate this to produce an output value, "average price".

In traditional spreadsheets, the semantic value of the numbers is lost. The number in cell B2 is not "the number of cars sold in January", but simply "the value in cell B2". The formula for calculating the average is based on the manipulation of the cells, in the form =C2/B2. As the spreadsheet is unaware of the user's desire for D to be an output column, the user copies that formula into all of the cells in D. However, as the formula refers to data on different rows, it must be modified as it is copied into the cells in D, changing it to refer to the correct row. For instance, the formula in D4 would read =C4/B4. Excel automates this later task by using a relative referencing system that works as long as the cells retain their location relative to the formula. However, this system requires Excel to track any changes to the layout of the sheet and adjust the formulas, a process that is far from foolproof.[11]

During the development of Improv, the Lotus team discovered that these sorts of formulas were both difficult to use and resistant to future changes in the spreadsheet layout.[12] Their solution was to make the user explicitly define the semantic content of the sheets that the B column contained "cars sold". These data ranges were known as "categories". Formulas were written by referring to these categories by name, creating a new category that could be (if desired) placed in the sheet for display. Using the car example, the formula in Improv would be average per car = total income / cars sold. Changes to the layout of the sheet would not affect the formulas; the data remains defined no matter where it is moved. It also meant that formulas calculating intermediate values did not have to be placed in the sheet and normally did not take up room. The downside to Improv's approach is that it demanded more information from the user up-front and was considered less suitable for "quick and dirty" calculations or basic list building.[13]

Numbers uses a hybrid approach to the creation of formulas, supporting the use of named data like Improv, but implementing them in-sheet like Excel. In basic operation, Numbers can be used just like Excel; data can be typed anywhere and formulas can be created by referring to the data by its cell. However, if the user types a header into the table, something one normally does as a matter of course, Numbers uses this to automatically construct a named range for the cells on that row or column. For instance, if the user types "month" into A1 and then types the names "January", "February", etc. into the cells below it, Numbers constructs a named range for the cells A2 through A13 and gives it the name "month". The same is true when the user types in the figures for "sales" and "income". The user can then write the averaging formula in a category-like text format, = total income / cars sold. The formula will find the appropriate data and calculate the results independent of the row.[14] Like Improv, this formula does not refer to the physical location of the data in the sheet, so the sheet can be dramatically modified without causing the formula to fail.[14]

Similar to Improv, formulas can be represented as icons in Numbers, allowing them to be dragged about the sheets. One noteworthy example of this is a sidebar that contains the sum, average, and other basic calculations for the current selection in the active table. These serve a function similar to the sum that appears at the bottom of the window in Microsoft Excel. However, the user can drag one of the function icons from the sidebar into the sheet to make the calculation appear in that location.[14] In another nod to Improv, the Formula List shows all of the formulas in the spreadsheet in a separate area and allows edits in place or easy navigation to their use in the sheets.

Numbers '09 contains 262 built-in functions that can be used in formulas.[15] This contrasts with Excel 2007's 338 functions.[16] Many of the functions in Numbers are identical to those in Excel; missing ones tend to be related to statistics, although this area was greatly improved in Numbers '09.[17]

Numbers '09 includes a system for categorizing data similar to pivot tables. Pivots were introduced in Improv and were manipulated by dragging the category headers,[17] allowing the user to quickly rotate rows into columns or vice versa. Although Numbers has similar draggable objects representing formulas, they are not used for this feature and the direct manipulation is missing. Instead, Numbers places pop-up menus in the column headers allowing the user to collapse multiple rows into totals (sums, averages, etc.) based on data that is common across rows. This is similar functionality to a pivot table but lacks the ease of re-arrangement of the Improv model and other advanced features. Numbers 5.2, released on September 17, 2018,[18] further improves on these features by adding Smart Categories, allowing the user to "quickly organize and summarize tables to gain new insights".[19]

Pivot tables were later added to Numbers 11.2 on September 28, 2021.[20]

### Layout and displayEdit

As Numbers uses the canvas as the basis for the document, media is not tied to the tables; one could build a Numbers canvas that contains a collection of photographs but no tables. In typical use, one or more tables are placed on the canvas and sized and styled to show only the data of interest. Charts and labels are commonly positioned around the tables. Other media, like photographs or illustrations, can be added as well.[21] Numbers' display-centric model has been referred to as a "page layout and presentation app disguised as a spreadsheet app".[22]

Like other products in the iWork suite, Numbers includes a variety of styles and layouts designed by professional illustrators. Opening an Excel sheet in Numbers results in a display with smooth fonts, clean layout and color selections. These can then be modified, optionally using one of the supplied templates, and saved out to Excel format again with these styles intact. Numbers also allows sheets to be emailed in Excel format in a single step or shared through Numbers for iCloud.