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In the previous chapter, you learned how to create the basic view controllers that fulfill the controller role of an MVC architectural model. You re now ready to start accepting user input, because you can send users to the correct object. Users can interact with your program in two ways: by using the low-level event model or by using event-driven actions. In this chapter, you ll learn the difference between the two types of interactions, and how to implement them. Then we ll look at notifications, a third way that your program can learn about user actions. Of these three models, events provide the lowest-level detail and ultimately underlie everything else (they re essential for sophisticated programs), so we ll begin with events.

To find the variability of a sample, you must compute its standard deviation. The standard deviation is derived from the variance. Both are values that represent the dispersion of the data. Of the two, the standard deviation is the most important because it can be thought of as the average of the distances between each value in the sample and the mean. The variance is computed as shown here:

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We briefly touched on the basics of event management in chapter 2. But as we said at the time, we wanted to put off a complete discussion until we could cover events in depth; we re now ready to tackle that job. The fundamental unit of user input is the touch: a user puts a finger on the screen. This may be built into a multitouch or a gesture, but the touch remains the building block on which everything else is constructed. It s the basic unit that we ll examine in this chapter. In this section, we ll look at how touches and events are related. Let s start by examining the concept of a responder chain.

When a touch occurs in an SDK program, you have to worry about what responds to the event That s because SDK programs are built of tens perhaps hundreds of different objects Almost all of these objects are subclasses of the UIResponder class, which means they contain all the functionality required to respond to an event What gets to respond The answer is embedded in the concept of the responder chain This is a hierarchy of different objects that are each given the opportunity, in turn, to answer an event message Figure 61 shows an example of how an event moves up the responder chain It starts out at the first responder of the key window, which is typically the view where the event occurred where the user touched the screen.

Here, N is the number of elements in the set, M is the mean, and Di is an individual value from the sample. It is necessary to square the differences of the mean from each element to produce a positive outcome. If the difference were not squared, the result would always be zero. The standard deviation is derived by finding the square root of the variance. Thus, the formula for the standard deviation is shown here:

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