TEXT Book ( QUESTIONS ARE AT THE BOTTOM )

Analytics, Data Science, & Artificial Intelligence: Systems for Decision Support: 11th Edition. Sharda, Delen & Turban. Pearson. 2020/.

Algorithms 201: An algorithm specifies a series of steps that perform a particular computation or task. Originally limited to mathematics, currently the word is strongly associated with computer science or data analysis. Algorithms resemble recipes. Recipes tell you how to accomplish a task by performing a number of steps. For example, to bake a cake the steps are: preheat the oven; mix flour, sugar, & eggs thoroughly; pour into a baking pan; etc. However, algorithm is a technical term with a more specific meaning than recipe, and calling something an algorithm means that the following properties are all true:

• An algorithm is an unambiguous description that makes clear what has to be implemented. In a recipe, a step such as Bake until done is ambiguous because it doesnt explain what done actually means. A more explicit description such as Bake until the cheese begins to bubble is better. In a computational algorithm, a step such as Choose a large number is vague: what is large? 1 million, 1 billion, or 100? Does the number have to be different each time, or can the same number be used on every run?
• An algorithm expects a defined set of inputs. For example, it might require two numbers where both numbers are greater than zero. Or it might require a word, or a list of even or odd numbers.
• An algorithm produces a defined set of outputs. It might output the larger of the two numbers, an all-uppercase version of a word, or a sorted version of the list of numbers.
• An algorithm is guaranteed to terminate and produce a result, always stopping after a finite time. If an algorithm could potentially run forever, it would be of no use.
• Most algorithms are guaranteed to produce the correct result. Its rarely useful if an algorithm returns the largest number 99% of the time, but 1% of the time the algorithm fails and returns the smallest number instead.
• If an algorithm imposes a requirement on its inputs (called a precondition), that requirement must be met. For example, a precondition might be that an algorithm will only accept positive numbers as an input. If preconditions arent met, then the algorithm is allowed to fail by producing the wrong answer or never terminating.

Here are four different characteristics of an algorithm that are important:

1. Does an algorithm actually exist to perform a given task?
2. If an algorithm is proposed to solve a task, are we sure that the algorithm works for all possible inputs?
3. How long does the algorithm take to run? How much memory space does it require?
4. Once we know its possible to solve a problem with an algorithm, a natural question is whether the algorithm is the best possible one. Can the problem be solved more quickly?

An Example Algorithm: Converting Fahrenheit temperature(s) to Celsius temperature(s) [(F - 32) x 5/9 = C]

1. Subtract 32 from the Fahrenheit temperature. (F) F 32 = FA (Fahrenheit Adjusted) [This brings the Fahrenheit freezing point down to zero, to coincide with the Celsius freezing point.] (FA) 2. Multiply the result by 5 and divide by 9 (i.e. multiply by 5/9). FA x 5/9 = C (Celsius Temperature) [This compresses the Fahrenheit scale so that each degree has the same size as one Celsius degree.] (C)

Problem: Given a Fahrenheit temperature of 72, what is the corresponding Celsius temperature?

72 32 = 40 40 x 5 = 200 200/9 = 22.22

Does this meet the criteria for being an algorithm?

• Is it unambiguous? Yes. Each step of the algorithm consists of primitive operations with easy translation.
• Does it have defined inputs and outputs? Yes.
• Is it guaranteed to terminate? Yes. The list F is of finite length (only one temperature/element is to be converted) so after looking at every element of the list the algorithm will stop.
• Does it produce the correct result? Yes. In a formal setting, you would provide careful proof of repeated accuracy.

The different characteristics of an algorithm that are useful to know:

1. Does an algorithm actually exist to perform a given task? Yes
2. If an algorithm is proposed to solve a task, are we sure that the algorithm works for all possible inputs? Yes
3. How long does the algorithm take to run? Less than 1 minute if computed manually How much memory space does it require? Unknown but minimal
4. Once we know its possible to solve a problem with an algorithm, a natural question is whether the algorithm is the best possible one. Can the problem be solved more quickly? Yes..much more quickly by program than manual calculation

Please see questions below.

7. Can you describe the content of the following 3 sections:

(a) Statistics Intro: Mean, Median, and Mode: (150-word minimum for each)

(b) Mean, median, and mode example; (150-word minimum for each)

(c) Choosing the "best" measure of center. (150-word minimum for each) (12 pts)