Questions and Answers
What is a frequency distribution?
What does frequency (f) represent?
Number of data entries in the class
What is the first step in constructing a frequency distribution?
Determine the number of classes (5-20)
What are class limits?
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What is relative frequency?
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What does cumulative frequency represent?
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What is a frequency histogram?
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How are class boundaries calculated?
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What is the method for calculating the midpoint of a class?
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What is an ogive?
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What is central tendency?
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What is the mean in statistics?
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How is median defined?
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What does mode represent?
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Study Notes
Frequency Distribution
- A frequency distribution organizes data into classes or intervals with counts for each class.
Frequency (f)
- Frequency represents the number of data entries within a specific class.
Constructing a Frequency Distribution
- Aim for 5 to 20 classes when creating a frequency distribution.
- Class width is determined by dividing the data range by the number of classes.
- Establish class limits; create tally marks for data entries within each class.
- Count tally marks to find the frequency for each class.
Class Limits
- The lower limit of the first class is the smallest data entry.
- Subsequent lower limits are derived by adding the class width to the previous class's lower limit.
- The upper limit for each class must ensure there is no overlap with adjacent classes.
Problem-Solving Steps for Data
- Identify the highest and lowest values in the data set, and calculate the range.
- Divide the range by the number of groups to find class width, rounding up if necessary.
- List all class limits starting from the lowest value, adjusting upper limits to avoid overlap.
- Use tally marks to record occurrences within each price range.
Relative Frequency
- Relative frequency represents the proportion or percentage of the data that falls into a specific class, calculated as class frequency divided by the sample size.
Cumulative Frequency
- Cumulative frequency is the running total of frequencies for a class and all preceding classes.
Frequency Histogram
- A graphical representation of frequency distribution using bars; horizontal axis for data values and vertical axis for frequency in classes.
Class Boundaries
- Class boundaries prevent gaps between classes, achieved by adjusting lower boundaries downward and upper boundaries upward by 0.5.
Midpoint
- The midpoint of a class is calculated by averaging its upper and lower limits.
Frequency Polygon
- A line graph depicting changes in frequency, starting and ending on the horizontal axis.
Relative Frequency Histogram
- Similar to a regular histogram, but the vertical axis represents relative frequencies as percentages.
Ogive (Cumulative Frequency Graph)
- A line graph representing cumulative frequency plotted against class boundaries.
Stem and Leaf Plot
- This plot separates numbers into a 'stem' (leading digits) and 'leaf' (trailing digits), facilitating visualization and sorting.
Dot Plot
- A visual representation where data values are indicated with dots above a number line.
Pie Chart
- A circle divided into sectors to represent categories; the area of each sector correlates with its frequency.
- Central angle of each sector is calculated as 360 degrees multiplied by its relative frequency.
Pareto Chart
- A bar graph showing frequency or relative frequency, arranged in descending order, with the tallest bar positioned on the left.
Paired Data Sets
- Each entry in one data set corresponds to another in a second data set, typically represented in scatter plots to demonstrate relationships between two quantifiable variables.
Time Series Graph
- A display of quantitative entries tracked over regular intervals; typically, dates are presented in order on the horizontal axis, with a line graph illustrating trends over time.
Central Tendency
- Measures the typical or central entry of a data set, calculable by mean, median, or mode.
Mean
- The mean is the average value computed by summing all entries and dividing by the number of entries.
Sigma Notation
- Represents the sum of all entries in a data set using the symbol ∑.
Median
- The median divides an ordered data set into two equal halves; it is the middle number for an odd count of entries and the average of the two middle numbers for an even count.
Mode
- The mode is identified as the entry with the greatest frequency; no mode exists if there are no repeats, and multiple modes occur if multiple entries appear with equal highest frequency.
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Description
Explore key concepts from Statistics Chapter 2 with these flashcards. This set covers essential terms like frequency distribution and methods for constructing frequency distributions. Perfect for reinforcing your understanding of data organization in statistics.
