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Frequency Distributions and Graphs - Analyzing Data Patterns

Learn how to construct frequency distributions and their graphs, including histograms, polygons, ogives, and relative frequency histograms.

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Frequency Distributions and Graphs - Analyzing Data Patterns

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  1. CHAPTER TWO DESCRIPTIVE STATISTICS

  2. Section 2.1 Frequency Distributions and Their Graphs

  3. Frequency Distribution • Def: a table that shows classes or intervals of the data entries with a count of the number of entries in each class, f. • Frequency Distributions may also include: • - Cumulative frequencies, cf. (running total) • - Relative frequencies, rf. (% of total) • - Class Midpoint (aka Class Mark) (sum of class limits, divided by 2)

  4. Find (a) class width, (b) class midpoints, and (c) class boundaries • Travel time to work (in minutes)

  5. Construct a Frequency Distribution: • Decide on the # of classes to include (between 5 and 20) • Find the class width: range of the data divided by the # of classes, round UP if needed. • Find the class limits: These are the lower and upper values for each class. Classes cannot overlap! • Tally the data to find the frequency, f, for each class.

  6. Construct a cumulative frequency distribution: • Daily saturated fat intakes (in grams) for a sample of people:

  7. Graphs of frequency distributions: • Frequency Histogram: a bar graph that represents the distribution. • 1. Horizontal scale = classes • 2. Vertical scale = frequencies of classes • 3. Consecutive bars touch - Use class BOUNDARIES on the horizontal scale. • Frequency Polygon: a line graph that emphasizes the continuous change in frequencies. (Must start and end at 0 to close the shape)

  8. Cumulative Frequency graph (OGIVE): a line graph that displays the cumulative frequency of each class at its upper boundary. • 1. Horizontal scale: first lower boundary and all upper boundaries of the classes. • 2. Vertical scale: frequencies • 3. graph goes from 1st lower boundary (cf = 0) to last upper boundary (cf = n)

  9. Relative Frequency Histogram: has the same shape as a frequency histogram, but uses the RELATIVE frequencies on the vertical axis.

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