Questions and Answers
What is a frequency table?
How do you find the class width?
(Largest - smallest)/desired number of classes
What are the lower and upper class limits?
The lowest and highest data values that can fit in a class, respectively.
What is tallying data?
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How do you find the midpoint of a class?
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How do you find class boundaries for integer data?
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What is relative frequency?
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What are the steps to create a frequency table?
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What does a mound shaped symmetrical distribution look like?
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A histogram is always symmetrical.
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What does the term 'skewed left' mean?
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What are outliers?
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What is cumulative frequency?
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What is an ogive?
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What is a histogram?
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Study Notes
Frequency Table
- A frequency table organizes data into classes or intervals of equal width, showing the count of data values in each class.
- Each data value must belong to exactly one class.
Finding Class Width
- Class width is calculated using: (Largest value - Smallest value) / desired number of classes.
- Always round up to the nearest whole number if the computed value isn’t whole.
- Common practice is to use between 5 and 15 classes.
Class Limits
- The lower class limit is the smallest data value within the class, while the upper class limit is the largest data value within the class.
- Class width is the difference between the lower class limits of adjacent classes.
Tallying Data/Class Frequency
- Tallying counts how many data values fall into each class.
- For tallying, each data value is examined, and a tally mark is made next to the corresponding class.
- The fifth tally mark is made diagonally across the first four for clearer counting.
Midpoint Calculation
- The midpoint, or class mark, is found by averaging the lower and upper class limits: (Lower class limit + Upper class limit) / 2.
Class Boundaries for Integer Data
- To find upper class boundaries, add 0.5 to the upper class limit.
- To find lower class boundaries, subtract 0.5 from the lower class limit.
Relative Frequency
- Relative frequency represents the proportion of total data values in a specific class.
- Calculated by dividing class frequency by the total number of observations (n): Relative Frequency = F/N.
- The sum of all relative frequencies across classes equals 1.
Creating a Frequency Table
- Establish the number of classes and calculate class width.
- Set the lower class limit of the first class as the smallest data value.
- Form subsequent classes by adding the class width.
- Count and tally data values into designated classes, and compute each class's frequency.
- Determine midpoints and class boundaries for all classes.
Mound-Shaped Symmetrical Distribution
- Mound-shaped histograms appear symmetrical when folded vertically down the center, indicating balanced data distribution.
Uniform Distribution
- Uniform or rectangular refers to histograms where each class has equal frequency.
- This distribution type is symmetrical, with all bars of equal height.
Skewed Distributions
- Skewed left (negative skew) indicates the left tail is longer; skewed right (positive skew) shows a longer right tail.
- The skew direction is identified by which side has the longer tail.
Bimodal Distribution
- Bimodal histograms have two peaks (high frequency classes) separated by at least one class, often suggesting data sampling from two distinct populations.
Outliers
- Outliers are data points that significantly deviate from the overall pattern of a dataset, indicating unusual observations.
Cumulative Frequency
- Cumulative frequency for a class is the cumulative total of frequencies for that class and all previous ones.
Ogive
- An ogive is a graph representing cumulative frequencies, offering a visual understanding of accumulated data.
Histogram
- Histograms visually represent data from frequency tables, using bars to depict each class.
- The width represents class width, while the height indicates class frequency for standard histograms and relative frequencies for relative frequency histograms.
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