The table below shows the number of rolls of film developed...

The table below shows the number of rolls of film developed for the United States media at the Winter Olympics. $$\begin{array}{|l|c|c|c|c|c|}\hline \text { Mmilizuonzatisticolizing } & 4 & 8 & 12 & 14 & 18 \\\hline \text { Eallsolitimple } & 48,200 & 53,750 & 60,500 & 67,500 & 75,000 \\ \hline\end{array}$$ a. Construct a scatter plot of the data. Describe the pattern of the number of rolls of film developed for the Winter Olympics from 1984 to 1998 . b. Writing Predict the number of rolls of film that will be developed for the Winter Olympics in the year $2002 .$ Explain how you made your prediction.

The table below shows the number of rolls of film developed for the United States media at the Winter Olympics.
$$\begin{array}{|l|c|c|c|c|c|}\hline \text { Mmilizuonzatisticolizing } & 4 & 8 & 12 & 14 & 18 \\\hline \text { Eallsolitimple } & 48,200 & 53,750 & 60,500 & 67,500 & 75,000 \\
\hline\end{array}$$
a. Construct a scatter plot of the data. Describe the pattern of the number of rolls of film developed for the Winter Olympics from 1984 to 1998 .
b. Writing Predict the number of rolls of film that will be developed for the Winter Olympics in the year $2002 .$ Explain how you made your prediction.

Key Concepts

Scatter Plot

A scatter plot is a graphical representation that uses dots to represent the values obtained for two different variables—one plotted along the x-axis and the other along the y-axis. It is useful for visualizing the relationship between these variables, identifying patterns, clusters, or possible correlations.

Trend Analysis

Trend analysis involves examining data over a period of time to discern any patterns or trends that may indicate a systematic increase or decrease. This process helps in understanding the underlying behavior of the dataset and can guide decision-making or predictions about future outcomes.

Linear Relationship

A linear relationship exists when two variables change at constant rates with respect to each other, meaning the data points tend to align along a straight line when graphed. Detecting a linear trend can simplify the process of prediction and analysis by allowing the use of linear models in evaluating the data.

Extrapolation

Extrapolation is the method of using established trends from known data points to estimate or predict values outside the current range of data. This technique is particularly useful when the pattern identified is consistent and is expected to continue into the future, though it carries the risk of increased uncertainty the further the prediction extends beyond the available data.

Transcript

00:01 Okay, for this problem, we were asked to create a scatter plot and then using all questions with that.

00:08 So let's make a scatter plot.

00:10 So the first step of a scatter plot, we need to draw our axes.

00:15 So more of an l -shaped axis, that.

00:21 Okay, and we're looking at a number of years since 1980.

00:28 We've got some film rules.

00:49 So the count is in years.

00:52 So we can almost go by ones here.

00:55 Actually go by two so then we got two four eight and twelve sorry okay i started over again let's just see how that looks and then over here we have rolls of film so we have kind of a pretty big number so we'll squiggly there and we'll start off with 40 ,000 and we have to go up to 75 ,000 so we'll save every two will be one so we'll go, that's 40 ,000, that's 50 ,000, 60 ,000, 70 ,000, 80 ,000.

02:12 So these are the year, these are the rolls of film.

02:24 And make sure to clarify that's in the thousands.

02:32 Okay, so now we have to graph it out.

02:34 So this is in 1984 to 1998.

02:37 So 4 is 48 ,200, and then 8 is 53 ,700.

02:52 1512 is 60 ,500.

02:58 14 is 67 ,500 and 18 is 75 ,000.

03:09 And 18 is 75 ,000.

03:15 Okay, so we can see the scatter plot, how it's increased pretty linearly, pretty uniformly.

03:21 That's our scatter plot, predict the number of roles will be developed in the year 2002.

03:26 Okay, so this is 1980 to 2002, that'd be 22 years.

03:35 So there's 20, so 22 would be about here.