Frequency Distribution: Key Terms
How do we turn a list of observations into a trustworthy frequency table and read what it says?
How this lesson unfolds.
Begin with How do we turn a messy list into information? The sequence then connects Ungrouped values or grouped classes? and builds toward Read the pattern, then keep the limitations.
How do we turn a messy list into information?
A raw list preserves every observation, but a frequency distribution reveals which values or ranges occur often.
- Learning goalExplain raw observations and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionUngrouped values or grouped classes?
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
Should every value get its own row?
Use individual values or categories when detail matters; use non-overlapping class intervals to summarize many numerical values.
- Learning goalExplain grouped versus ungrouped and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionValue, category and class are different
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
What exactly can a frequency count describe?
A value is one observed number, a category is a label, and a class is a numerical interval containing multiple possible values.
- Learning goalExplain core vocabulary and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionChoose enough classes to show shape
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
How many classes should a grouped table use?
Too few classes hide structure and too many recreate the raw list; five classes are a readable choice for this 20-value example.
- Learning goalExplain number of classes and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionClass width divides the covered range
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
How wide should each class be?
Choose a convenient width at least as large as range divided by number of classes, then verify the classes cover every observation.
- Learning goalExplain class width and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionClass limits label the intervals
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
Where does each class begin and end?
For whole-dollar prices, inclusive limits 1500-1599, 1600-1699 and so on form five non-overlapping classes.
- Learning goalExplain class limits and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionBoundaries remove apparent gaps
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
Why can limits and boundaries differ?
For data rounded to the nearest dollar, subtract and add 0.5 to get continuous boundaries such as 1499.5-1599.5; alternatively use half-open intervals such as [1500,1600).
- Learning goalExplain class boundaries and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionA midpoint represents one class
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
What single value can stand for an interval?
The class midpoint is the average of its two boundaries or limits; for 1500-1599 it is 1549.5.
- Learning goalExplain class midpoint and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionTallies become absolute frequencies
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
How do we count observations without losing any?
Place each observation into exactly one class, mark a tally, and convert the tallies into absolute frequencies whose total equals n.
Place each observation into exactly one class, mark a tally, and convert the tallies into absolute frequencies whose total equals n.
- Learning goalExplain tally and frequency and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionRelative frequency compares shares
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
What proportion of observations lies in each class?
Relative frequency is class frequency divided by n; multiplying by 100 expresses the same share as a percentage.
- Learning goalExplain relative frequency and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionCumulative frequency keeps a running total
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
How many observations are at or below a class?
Add frequencies from the first class through the current class; the final cumulative frequency must equal n.
Add frequencies from the first class through the current class; the final cumulative frequency must equal n.
- Learning goalExplain cumulative frequency and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionA complete table can check itself
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
How do we know the table is internally consistent?
Absolute frequencies sum to n, relative frequencies sum to 1 or 100 percent, and the last cumulative frequency equals n.
Absolute frequencies sum to n, relative frequencies sum to 1 or 100 percent, and the last cumulative frequency equals n.
- Learning goalExplain table validation and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionChoose a graph that matches the data
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
When is a bar chart not a histogram?
Bar charts separate categories; histograms join numerical intervals. With unequal interval widths, histogram height must be frequency density, frequency divided by width.
- Learning goalExplain graphs and density and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionThe vocabulary forms one connected system
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
How do all the frequency terms fit together?
Class design determines where observations go; counts create frequencies; frequencies create proportions, cumulative totals and graphs.
- Learning goalExplain concept map and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionRead the pattern, then keep the limitations
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.
What can a frequency distribution tell us?
It reveals common ranges, concentration and possible shape, but grouping loses within-class detail and depends on the chosen boundaries.
- Learning goalExplain interpretation and recap and apply it correctly in a frequency distribution.
- Helpful foundationscounting · fractions · percentages
- Common trapClasses must not overlap; histogram bars represent numerical intervals, and unequal widths require frequency density so area represents frequency.
- Next connectionBuild and interpret a frequency distribution from a new dataset
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The portrait diagram gives a definition, three checks, a worked price example, and one conclusion.