In this lecture, I'll be demonstrating for you the use of some of the built-in functions in Excel and in Google Sheets. We'll be using some of these functions because they're included throughout the Business and Financial Modeling specialization. They include functions like sum and sumproduct, as well as statistical functions like average, minimum, maximum, and standard deviation. In order to practice these new functions, let's explore another new business opportunity. This one involves the manufacture of an innovative speaker design. So let's turn back to the computer. Amy, a professional engineer, has a new venture called Innovative Speakers. She has a new design for an audio speaker and has contracted with a manufacturer to handle the production of small quantities as she builds up her business. This spreadsheet displays the component parts needed in the manufacture. They include cabinets, diaphragms, electronics, electrical components, and there's also a cost for assembly. To see the total cost of a single unit, we could use the sum function. But in this case I'll use an alternative, the sumproduct function. Sumproduct takes as its argument or arguments an array or a set of arrays. In this case, I will take the range or array from B5 to F5, And see the product of that range multiplied against a second array, B6 to F6. And the result of the total cost for the production run we're looking at here is $1830. The advantage to sumproduct over sum is the fact that we've reduced the number of equations. So instead of using six sum equations, we now use one sumproduct equation in a single cell. To show you a slightly more complicated use of sumproduct, I'm going to move to a second sheet, to sheet two. This sheet shows a weekly ledger of sales of Amy's speakers. Sumproduct can calculate multiple arrays or ranges from the sales ledger. In this example, our sales ledger shows units of speaker type A and speaker B each week. The prices of each speaker vary and notice that we raised prices in March. In this case, the sumproduct function calculates units A and units B as one array. And multiplies it against price A and price B as a second array, to come up with the sum of $6905, again, reducing the number of formulas and the chance for error. For now, let's look at some of Excel's built-in statistical functions with this same data. At the bottom of this sheet three I've included some output cells to demonstrate the average number of sales per week, as well as a minimum and maximum number. I've also included a standard deviation formula to show how much variance is from week to week. So in this case I've used the average function, one of the built-in statistical functions in Excel, with the range B3 to B15. In the same way, I've used that range to identify the minimum value that might appear in that range, as well as the maximum value, using the built-in functions MIN and MAX. Standard deviation comes in various forms. STDEV.P is for the entire population that exists in that range. And the larger the standard deviation, the larger the variance between one week and the next, the larger the variety of sales levels that we have to contend with. These numbers help Amy think about how many speakers she needs to manufacture to meet demand. She doesn't want to overbuild. There are costs to storing inventory, and she's always improving designs. In another module we'll look at how to best determine the most optimal production decisions given those constraints.