A questionnaire provides 58 Yes, 42 No, and 20 No-Opinion answers. a. In the construction of a p

A questionnaire provides 58 Yes, 42 No, and 20 No-Opinion...

Key Concepts

Bar Chart Construction

A bar chart represents categorical data with rectangular bars where the height (or length) of each bar is proportional to the frequency of the category it represents. This enables straightforward comparisons between different categories and is another common method for visualizing frequency distributions.

Pie Chart Construction

Constructing a pie chart relies on dividing a circle into sectors where each sector's angle is determined by multiplying its corresponding proportion of the total data by 360 degrees. This visual tool is used to show the relative proportions of categorical data in a clear, intuitive manner.

Proportional Reasoning

Proportional reasoning is the process of determining the part-to-whole relationship by dividing the number of responses in one category by the total responses. This is crucial when converting these proportions into other forms such as angles in a pie chart, ensuring that each category’s graphical segment accurately reflects its relative frequency.

Frequency Distribution

This concept involves organizing data into categories and representing each category's frequency. In the context of the problem, the number of 'Yes', 'No', and 'no-opinion' responses is counted and used to determine the proportions for visual representation.

Transcript

00:01 Okay, so for this question, it tells us that we've got a questionnaire with different responses.

00:05 So our yes responses are 58 and our noes are 42.

00:12 And of course, we also have some people with no opinion who account for 20 of the votes.

00:19 Now, in a, it wants us to create a pie chart, but we just want to know the proportion of the pie chart that's represented by the yes answers.

00:28 So if we're going to figure out what proportion of the pie chart is represented by the yes answers, we need to figure out what proportion of the total is represented by the yes answers.

00:36 So to find our proportion of yes, we would want to take 58 and divide it by the total, which i haven't quite figured that out yet.

00:49 We can do that right now.

00:50 So the total would just be 58 plus 42 plus 20.

00:58 And that gives us 120.

01:02 So over here, where i wrote total, i can just erase that and write 120.

01:06 And 58 out of 120 is, let me just do that in my calculator real quick.

01:12 Well, it's a continuous decimal.

01:14 It's 29 out of 60, which is approximately 0 .483.

01:19 However, i like to be really precise, so i'm going to leave it as 29 .0 .60.

01:23 So about 48 % or 29 out of 60 of the circle is going to be represented by the yes.

01:30 So we have to think back about to our geometry days and think about how many degrees are in a circle, and that's 360.

01:36 So in the circle, we've got 360 degrees.

01:41 And we want 2960th to be represented, 2960th of the 360 degrees to be represented by the yes.

01:50 So we'll just do that in our count.

01:53 Calculator real quick, and that's 174 degrees.

01:57 So the proportion that's yes is going to be 174 degrees.

02:03 Now, part b asks us how many degrees would be in the no.

02:10 So of course, we want to do the same kind of thing.

02:12 We want to find the proportion no, which is going to be 42 out of 120.

02:18 And that gives us about exactly 35%.

02:23 So to find...

02:25 What proportion of the circles represented by that.

02:27 We just do 360 degrees, which is the total degrees in the circle, then multiply it by 35%.

02:32 And we get 126 degrees.

02:38 Okay, now that we have those two things, the question thinks that we're ready to make a pie chart.

02:43 So that's what we're going to do.

02:44 So we are going to draw a circle.

02:49 Now, i've got to be honest, i'm not going to be able to make it perfect on here, but i'm going to get it as close as possible.

02:55 So my yes is, almost half a circle.

02:59 So i'm going to draw half the circle and then just kind of put the center in there.

03:03 Now it kind of looks like a pokemon ball.

03:05 And i got about 174.

03:09 So now if you were being an extra precise student, you'd want to whip out your protractor right now that i know you all have in your pockets.

03:17 And you would want to measure 174 degrees.

03:20 However, i don't have that right now.

03:23 Okay.

03:23 So then the no proportions 126, which is about two thirds.

03:27 A little over two thirds of the other half of the circle.

03:30 So i'm going to draw about two thirds of the other half of the circle.

03:34 So maybe this looks like one third.

03:37 This is two thirds.

03:39 That's close.

03:40 Again, you would want to get out your protractor at this point and it would be extra precise.

03:45 This would be 126 degrees...

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