Questions and Answers
What is a frequency distribution?
What is the lower class limit?
smallest number in each given class
What is the upper class limit?
largest number in each given class
What does class width refer to?
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How is range defined?
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What are the steps to construct a frequency distribution from a data set?
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What is the midpoint of a class?
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What does relative frequency measure?
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How is cumulative frequency defined?
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What is a frequency histogram?
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What does the horizontal scale on a frequency histogram represent?
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What does the vertical scale on a frequency histogram measure?
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What are class boundaries?
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What is an ogive?
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What is a frequency polygon?
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What are the steps to create a frequency polygon?
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What does a relative frequency histogram measure?
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What is a cumulative frequency graph or ogive?
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Study Notes
Frequency Distributions
- A frequency distribution is a table showing classes or intervals of data with counts for each class.
- The lower class limit indicates the smallest number in a given class.
- The upper class limit specifies the largest number in a given class.
Class and Range Concepts
- Class width is calculated by finding the difference between consecutive lower or upper limits, and dividing the range by the number of classes; always round to whole numbers.
- Range is determined by subtracting the minimum data entry from the maximum: Range = Maximum - Minimum.
Constructing a Frequency Distribution
- Choose the number of classes, typically between 5 to 20.
- Calculate class width and establish class limits.
- For class limits: the first lower limit is the minimum value; subsequent lower limits are calculated by adding the class width to the previous lower limit. The upper limit is one unit less than the next class's lower limit.
- Determine frequencies for each class.
Midpoints and Frequencies
- Midpoint of a class is computed as the average of the lower and upper limits: Midpoint = (Lower + Upper) / 2.
- Relative frequency represents the proportion of data falling into a class: Relative Frequency = Class Frequency / Sample Size.
Cumulative Frequency
- Cumulative frequency is the total frequency for a class and all previous classes; the final class's cumulative frequency equals the sample size.
Graphical Representations
- A frequency histogram is a bar graph depicting frequency distributions, where consecutive bars align in width.
- The horizontal scale of a histogram represents quantitative and measurable data values.
- The vertical scale measures the frequencies of the classes.
- Class boundaries eliminate gaps between classes: lower boundary = Lower Limit - 0.5, upper boundary = Upper Limit + 0.5.
Ogives and Polygons
- An ogive is a graph illustrating cumulative frequencies.
- A frequency polygon is a line graph showing continuous frequency changes, plotted using midpoints and frequencies.
Constructing a Frequency Polygon
- Choose horizontal axes for midpoints and vertical axes for frequencies.
- Plot points for midpoints and frequencies, connect these points, and extend as necessary.
- Start plotting at the first class midpoint minus class width and end at the last class midpoint plus class width.
Relative Frequency Histogram
- A relative frequency histogram plots relative frequencies on the vertical axis.
Cumulative Frequency Graph (Ogive)
- An ogive line graph displays cumulative frequencies at upper class boundaries, using upper boundaries on the horizontal axis and cumulative frequencies on the vertical axis, without descending back to the horizontal axis.
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Description
Explore essential concepts from Statistics Chapter 2.1 with these flashcards. Learn about frequency distributions, class limits, and more terminology crucial for understanding data organization. Perfect for studying and reinforcing statistical knowledge.