Questions and Answers
What is a frequency distribution?
What is the first step in constructing a frequency distribution from a data set?
Decide on the number of classes to include in the frequency distribution.
Define the lower limit and upper limit in a class.
The lower limit is the least number that can belong to the class, and the upper limit is the greatest number that can belong to the class.
What does class width represent?
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How is the range calculated?
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What is the midpoint of a class?
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What is relative frequency?
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What is cumulative frequency?
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A histogram must have the vertical scale measure the data values.
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What do class boundaries ensure in a histogram?
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How is a frequency polygon created?
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A relative frequency histogram has a different shape compared to a frequency histogram.
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What is an ogive?
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What is a stem-and-leaf plot?
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Study Notes
Frequency Distribution
- A frequency distribution is a table that organizes data entries into classes or intervals, showing the number of entries in each class.
- Frequency (f) of a class refers to the count of data entries within that class.
Constructing a Frequency Distribution
- Determine the number of classes, ideally between 5 and 20, to detect patterns effectively.
- Calculate class width by finding the range of the data, dividing it by the number of classes, and rounding up.
- Identify class limits by using the minimum entry as the first class's lower limit and ensuring no overlap between classes.
- Tally each data entry in the corresponding class row to count frequency.
Class Limits
- Each class has a lower class limit (the smallest value in the class) and an upper class limit (the largest value in the class).
Class Width
- The class width represents the distance between the lower (or upper) limits of consecutive classes.
Range
- The range is the difference between the maximum and minimum values in a data set.
Midpoint
- The midpoint of a class is calculated as the average of the lower and upper class limits, providing a representative value for the class.
Relative Frequency
- Relative frequency indicates the portion or percentage of the total sample size that falls within a specific class, calculated by f/n.
Cumulative Frequency
- Cumulative frequency is the sum of frequencies for a class and all preceding classes, with the last class equaling the sample size.
Frequency Histogram
- A histogram visualizes frequency distribution using bars where the horizontal axis represents data values and the vertical axis shows frequency.
- Bars must be consecutive and touch each other.
Class Boundaries
- Class boundaries are numbers that separate classes in a histogram to eliminate gaps, ensuring bars touch.
Frequency Polygon
- A frequency polygon is a line graph used to depict frequency distribution, highlighting changes in frequencies across classes.
Relative Frequency Histogram
- This type of histogram shares the same shape and horizontal scale as a frequency histogram, but measures relative frequencies on the vertical axis.
Cumulative Frequency Graph (Ogive)
- An ogive is a line graph that illustrates cumulative frequency at each class's upper boundary, with upper boundaries on the horizontal axis and cumulative frequencies on the vertical.
Constructing an Ogive
- Start with a frequency distribution that includes cumulative frequencies.
- Specify horizontal (upper boundaries) and vertical (cumulative frequencies) scales.
- Plot and connect points representing upper boundaries and cumulative frequencies, starting from a cumulative frequency of zero.
Stem-and-Leaf Plot
- Stem-and-leaf plots are methods for displaying quantitative data and are part of exploratory data analysis (EDA) techniques developed by John Tukey.
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Description
This quiz features flashcards based on Chapter 2 of Statistics, focusing on key concepts such as frequency distributions and their construction from data sets. Perfect for students looking to reinforce their understanding of statistical data organization.
