PSDA - Making Inferences From Data Lesson
Making Inferences from Data
Data tells a story and provides information from which informed conclusions may be drawn. Different types of organization methods are used for the data depending on the type of data to be shown and analyzed. Organization methods could be linear, bar, tables. Information may be only words initially. Data organization will allow you to draw conclusions or make conjectures concerning your business operations, and allow you to foresee changes needed.
Linear Graph Data Inferences
Data displayed on graphs provide information from which further data or analysis may be obtained. Use the Amusement Ride Graph below to answer questions concerning the data shown on the graph by the data points and the conclusions drawn from connecting the data points. For this example, the number of people at the line grew linearly between all points. The ride opened at 9 a.m. Rain occurred during the day.
Amusement Park Bar Graph
Now let's look the bar graph of the Amusement Ride data below, a different method of displaying data. Does the bar graph provide the same perspective of the data? No, this graph only shows the number of people in line at each hour with no visual connection between the time periods. Yes we can still see when the times were increasing and decreasing. However, the connectivity of the line graph provides an idea of what happens during the times in between the hours and this is not clear on the the bar graph.
A bar graph is better with static or fixed data versus flexible, changeable data that is shown in the line graph above.
Here is a bar graph with static data.
ABC High School's basketball team has played 6 of their 20 games for the season. Scores for ABC and their opponent are shown in the bar chart below.
XYZ Company manufactures widgets for various customers throughout the world. The daily shipping schedule requires widgets to be shipped in bundles of 5 widgets. The number of widget bundles shipped for Monday through Friday for a period of 4 weeks is shown in the table below. Create a frequency table (histogram) of the data for the number of shipped bundles. For example, Week 1 on Monday, 12 bundles of 5 widgets are shipped, meaning 60 widgets are shipped.
| M | T | W | TH | F | |
|
Week 1 |
12 |
8 |
7 |
6 |
8 |
|---|---|---|---|---|---|
|
Week 2 |
7 |
6 |
8 |
10 |
11 |
|
Week 3 |
13 |
7 |
10 |
12 |
10 |
|
Week 4 |
12 |
12 |
8 |
8 |
7 |
To create a frequency table, a table of the number of times the widget bundle occurs, the number of widget bundles shipped will be used as the horizontal axis and the number of times shipped the vertical axis. Changing the type of graph allows a different perspective of the information. Changing to a frequency table provides a synopsis of common amounts shipped.
Scatter Plots
Scatter plot graphs are just that, the data points on a graph, unconnected, ready for interpretation. These points provide the relationship between the horizontal data and the vertical data and are plotted based on the (x, y) values.
Questions that are asked about scatter plot graphs usually look for positive and negative correlation and a regression index r. Data in scatter plots are graphed with two variables. The key to answering scatter plot questions is to determine whether there is a correlation (a match) between the data that suggests an outcome for future data.
Equations of the lines for scatter plots are called Regression Lines of Best Fit. The "line" that is requested could take on linear, exponential, or other math lines that connect data. The lines may be done by hand, but a graphing utility is best as the graphing utility can provide the regression index quickly when requested. Check your graphing utility to know the procedure for finding these regression lines and correlation index.
Let's look at a few scatter plots and answer some basic questions of understanding. For each of the graphs, estimate the line of best fit. In other words, where do you see a line or curved line going through the points so that the line is close to the maximum number of points? Once the line is drawn, determine the correlation and the strength of the correlation, the regression index r.
Positive correlation - a positive slope, use r correlated to visual sighting of slope
- visually sighted as with a correlation r = 1 if the points are grouped closely to the line shape, the strength of the correlation is strong
- visually sighted r = .5 if the points are follow the path of the line but are loosely associated with the line
Negative correlation - a negative slope, use r correlated to visual sighting of slope
- visually sighted as with a correlation r = −1 if the points are grouped closely to the line shape, the strength of the correlation is strong
- visually sighted r = −.5 if the points are follow the path of the line but are loosely associated with the line
No correlation - there is not a pattern positive or negative that can be found for the points plotted
- visually sighted as with a correlation r = 0, the points are scattered on the graph
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