Calculating and comparing an exact value with a practical value

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today, we're going to learn how to calculate and compare an exact value with a practical value.  Here's our problem statement: A polling company reported that 19% of 1,018 surveyed adults said that pesticides are “very harmful.”  Complete Parts A through D below.

Part A: Find an exact value

What is the exact value that is 19% of 1,018?

Well, here in this case, to solve this question, we're going to translate the English into math.  So we're looking for the exact value, so we could call that X or whatever you want to call it.  Is translates into an equal sign.  19% — we can convert that to decimal form so we can perform a mathematical calculation.  Of translates into multiplication.  And 1018 is a number we're going to multiply by.

So I'm just going to go over here to my calculator, and we're gonna multiply 19% — just 0.19 (just move that decimal point over two places to the left to convert from a percent to a decimal) — of is times 1018.  That gives us 193.42, so that's what I'm gonna put here in my answer field.  Good job!  Next part . . . .

Part B: Interpret an exact value

Could the result from Part A be the actual number of adults that have said that pesticides are “very harmful”?  Why or why not?

Well, if you want the actual number of adults, you're talking about discrete data because we don't count partial people.  We count people as whole values, so the actual number of adults is going to be an integer value.  The exact value 193.42 is not a whole number; it is a decimal.  And so this represents what we call continuous data.

So the answer to the question here in Part B is going to be “No” because we're only counting whole people.  So right off the bat we can eliminate answer options A and D.  So let's look at answer options B and C.

B says, “No, the result from Part A could not be the actual number of adults who said that pesticides are very harmful because that is a very rare opinion.”  No, we're actually talking about the difference between discrete and continuous data, so that doesn't sound right.

Let's look at answer option C: “No, the result from Part A could not be the actual number of adults who said that pesticides are very harmful because a count of people must result in a whole number.”  Bingo!  That's what we're looking for — “must result in a whole number” so that gives us discrete data.  We check our answer.  Good job!

Part C: Find a practical value

What could be the actual number of adults who said that pesticides are “very harmful”?

Well, to get the actual number, we're just gonna look at the exact value that we calculated here, and we're going to round it.  So 193.42 rounded to the nearest whole number — we're gonna go down because the number right after our decimal point is less than five.  So that gives us 193, which we type here in our answer field.  Well done!  And now the last part . . . .

Part D: Find a percentage

Among the 1018 respondents, 373 said that pesticides are “not at all harmful” — I’m not sure what they're . . . they're probably like, you know, making some sort of drug out of the pesticide and snorting it or something ‘cause I don't know how you can say pesticides are not at all harmful.  It's a . . . it's a . . . it's a processed chemical, man!  It's gonna . . . it's gonna have some harm to it!  But anyway that — that's what they said.  We’re not here to judge; we’re just here to take the data and do the stats with it.  So 373 said that they were not at all harmful.  What percentage of respondents said that pesticides are not at all harmful?

So if we want a percentage from the raw data, we just take the part and divide by the whole.  So the part is the 373; that's the part of the whole 1018 respondents in the group.  So I'm just gonna come over here, clear out my calculator, take 373 (that's the part) divided by the whole (1018), and boom!  There's our answer!

Now this is the percentage in decimal form.  Notice that here in the answer field, we're asked to calculate a percent; it wants the answer in percent form.  So I can move this decimal point in my head and put this in, but it says rounded to two decimal places.  So just to make sure I put the right number in, I'm going to come in and multiply this number by 100.  So then I convert from decimal to percent.  So now here's my percent which I can round the two decimal places — 36.64 — so that's what I'll stick in here.  Good job!

And there it is. That's the solution to each step of the problem.  That's how we do it here at Aspire Mountain Academy.  Be sure to leave your comments below to let us know how good a job we did or how we can improve.  And if your stats teacher is boring or just doesn't care to help you learn stats, go to aspiremountainacademy.com where you can find out more about accessing our lecture videos or provide feedback on what you'd like to see.  Thanks for watching, and we'll see you in the next video.