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- 1Qualitative datacan be organized and displayed using tables and graphs
- 2Tablesshowing counts (frequencies) and percentages or proportions (relative frequencies)
- 3Bar GraphsThe length of the bar for each category is proportional to the number or percent of
individuals in each category. Bars may be vertical or horizontal. - 4Pie Chartscategories of data are represented by wedges in the circle proportional in size to the percent
of individuals in each category. A pie chart can be used when you are trying to display the relationship between parts and the whole and can be effective if you have qualitative data that fall into only a few categories. - 5Example: A group of 28 students were asked whether or not they smoke. The following data set was obtained: Y Y Y Y Y Y Y Y Y Y Y N N N N N N N N N N N N N N N N N This data set can be organized into a frequency table by counting the number of yes and no responses.Example: A group of 28 students were asked whether or not they smoke. The following data set was obtained:
Y Y Y Y Y Y Y Y Y Y Y N N
N N N N N N N N N N N N N
N N
This data set can be organized into a frequency table by counting the number of yes and no responses. - 6Here is a bar chart with frequency on the vertical axis.
- 7Here is a bar chart with relative frequency on the vertical axis.
- 8Here is a pie chart.
- 9Quantitative DataQuantitative data can also be organized and displayed using tables and graphs. Quantitative data may be presented individually (ungrouped) or grouped into intervals.
- 10Quantitative DataExample: A group of 28 high school students were surveyed and asked the number of miles they live from their high school. The following data set was obtained:
1 1 1 2 2 2 2 3 3 3 3 3 3
3 4 4 4 4 4 4 4 4 5 5 5 5
5 5
Create an ungrouped frequency table for the data.
This is called an ungrouped frequency table because there are individual values in the first column.
There are five classes in this table since there are five rows (not including the column heading). - 11Histograma graph that consists of contiguous boxes (i.e. the edges of the boxes touch). The horizontal axis is labeled with what the data represents. The vertical axis is labeled with either “frequency” or “relative frequency.”
- 12Histogram ExampleFor the above example, create a histogram. Label the horizontal axis as “miles” and the vertical axis as “frequency.”
Example: A bank manager reported the following waiting times in minutes for a sample of customers.
1 0 0 3 4 2 2 3 1 2 3 1 0 0
2 3 0 5 3
Create an ungrouped frequency table and a histogram.
Solution: - 13The first column of a grouped frequency table consists of intervals of numbers (instead of individual numbers). We can also call these intervals “classes” or “bins.” It is very important that each observation be counted only in one class.Example: A group of 28 students were asked about the amount of sleep they received the previous night. The following data were obtained:
1 3 4 4 5 5 5 6 6 6 6 7 7
7 7 7 7 7 8 8 8 8 8 8 8 9
9 10 - 14Questions:How many students got 7 hours of sleep or more? __________________________________________
What proportion of students got less than 3 hours of sleep? ___________________________________________ - 15Stemplots-A graph for which every number is split into two parts—a stem and a leaf. It allows us to reconstruct the original data if desired. Stemplots work well for small data sets, but not as well for large data sets.
- 16DotplotA dotplot is a graph in which each data value is plotted as a point (or dot) along a scale of values.
- 17ExampleThe following dotplot shows the number of pages viewed on a website by an individual visitor.
- 18When looking at a graphical display of data, it’s a good idea to examine the following features:• Center—What is a typical value in the data set?
• Spread—Are the values clustered tightly together or are they spread out?
• Gaps—Are there areas in the graph where there are no values?
• Outliers—Are there extreme values?
• Shape—Is there a pattern to the data? See below. - 19Symmetric—One side is (approximately) a mirror image of the other. The example below is a bell-shaped, symmetric distribution.
- 20Uniform—Every class has equal frequency.
- 21Skewed Left—The distribution has a long left tail.
- 22Skewed Right—The distribution has a long right tail.
- 23Bimodal—The distribution has two peaks.
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- Flashcards on Untitled, created by Max Goodman on 04/02/2019.
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