LGT5101 Chap.2 Frequencies, Charts and Histograms
Frequencies, Charts and Histograms
Choose the picture from the variable
Frequency tables compress raw records into counts and relative frequencies. Counts show workload, while relative frequencies place groups with different totals on a common denominator. Both need a checksum: class counts must reconcile with the usable observations and relative frequencies must sum to one, subject only to rounding.
Missing values, filters and the observation window belong beside the denominator.
Keep categories and measurements distinct
Categorical values use separated bars or, for a small partition of one whole, pie slices. Bar length supports precise comparison, whereas pie angle is harder to judge when slices are numerous or similar. Preserve a natural ordering for ordinal categories.
Reordering nominal categories can highlight rank, but it must not imply a measurement scale that the labels do not possess.
Treat histogram bins as analytical choices
Quantitative values use non-overlapping intervals with touching bars. Histograms sacrifice exact observations to reveal centre, spread, shape, clusters and gaps. Bin boundaries require an inclusion rule so each value enters exactly one interval.
Width matters: very broad bins can erase a second cluster, while very narrow bins can turn sampling variation into apparent structure. Equal widths let height represent frequency directly; unequal widths require density so area remains proportional to count.
Interpret pattern before mechanism
Every display needs an informative title, labelled axes and a stated frequency scale.
Describe a quantitative shape through centre, spread, skewness and unusual features, then name the operational check suggested by that pattern. A second peak may justify splitting the data by shift or service type, but the chart alone does not prove the split caused the pattern.
A defensible display makes structure visible, preserves the denominator and ends with a testable next question rather than an invented causal story.
What this chapter covers
- 01
Class frequency
- 02
Relative frequency
- 03
Bar charts for categories
- 04
Pie charts for a whole
- 05
Histogram intervals
- 06
Bin width decisions
- 07
Pattern without causation
Worked example · free
Display channel and time
- 3Build channel relative frequencies.
- 2Choose a categorical display.
- 3Define time bins and the histogram reading.
Key terms
- Class Frequency
- The number of observations falling in a category or interval.
- Relative Frequency
- A class frequency divided by the total observation count.
- Bar Chart
- A display using separated bars for categorical classes.
- Histogram
- A display grouping quantitative values into adjacent intervals.
- Bin Width
- The numerical span covered by one histogram interval.
Frequencies, Charts and Histograms FAQ
Why do histogram bars touch?
Each bar occupies an adjacent interval on one continuous measurement scale, so the bars meet at their boundaries. Categorical bars remain separated because the categories are distinct classes rather than neighbouring sections of a numerical line.
How many histogram bins should I use?
The lecture material normally suggests at least five and no more than fifteen classes, while noting that the useful number depends on how many values are available. Compare reasonable widths and choose one that reveals structure without turning random noise into a pattern.
Can a chart prove why a pattern occurred?
No. A chart can reveal concentration, skewness, gaps or several clusters, but it does not establish the process causing them. Use the visible pattern to identify the next operational split or data check, then test that explanation with additional evidence.
Exam move
Build one frequency table from a categorical column and one histogram table from a quantitative column. Check the category total and the histogram total against the raw row count. Redraw the histogram with a second reasonable width and note which features persist. Write one interpretation sentence that names the pattern and one follow-up question without asserting a cause.
Recalculate relative frequencies after removing missing observations and write the new denominator beside every percentage. For the histogram, specify half-open interval notation and test every boundary value to confirm it enters exactly one bin. Compare a broad and narrow bin width, identifying centre, spread, skew, clusters and gaps that survive both views.
Then deliberately create three misleading versions: a truncated bar axis, unordered ordinal categories and a histogram with ambiguous boundaries. Repair each version and explain what false impression the original geometry could create. End with a short management caption that states the population, time window, visible pattern and next operational check.
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