Question 1

What is a frequency distribution?

Accepted Answer

A frequency distribution is a table that shows how many times each value or range of values appears in a dataset. For discrete data (counts, categories, integers), each unique value gets its own row. For continuous data (measurements), values are grouped into class intervals (bins) of equal width. The distribution reveals the shape of the data — whether it is symmetric, skewed, bimodal — and is the data behind a histogram.

Question 2

What is the difference between absolute and relative frequency?

Accepted Answer

Absolute frequency is the raw count of how many times a value appears in the dataset. Relative frequency is the proportion: absolute frequency / total n, expressed as a decimal or percentage. Relative frequency is more useful for comparing datasets of different sizes. Cumulative relative frequency sums these proportions from the smallest to largest value, reaching 1.0 (100%) at the last row.

Question 3

How do I choose the number of class intervals for continuous data?

Accepted Answer

Several rules exist: Sturges' rule: k = 1 + 3.322 × log₁₀(n). Square root rule: k = √n. Rice rule: k = 2 × n^(1/3). For n=50, these give roughly 7, 7, and 7 classes. As a rule of thumb, 5–15 classes work well for most datasets — too few hides the shape; too many produces a noisy table with many empty cells. The class width = (max − min) / k, rounded to a convenient number.

Question 4

What is cumulative frequency used for?

Accepted Answer

Cumulative frequency shows how many observations fall at or below each value. It is used to: read off percentiles (the value at which cumulative frequency = 50% is the median); assess the proportion of the sample below any threshold (e.g., what fraction scored below 70?); and construct ogive curves (cumulative frequency graphs) for distribution fitting.

Question 5

How is a frequency distribution related to a histogram?

Accepted Answer

A histogram is the graphical representation of a frequency distribution for continuous data. Each bar's height equals the frequency (or relative frequency) of the corresponding class interval. The area of each bar is proportional to frequency when class widths are equal. The shape of the histogram directly reflects the shape of the frequency distribution — and reveals whether the data is symmetric, skewed, bimodal, or uniform.

Question 6

Can I compute a frequency distribution for categorical data?

Accepted Answer

Yes — for categorical (nominal) data, a frequency distribution is simply a count of how many times each category appears. The 'relative frequency' column gives the proportion in each category. You cannot compute cumulative frequency meaningfully for nominal data (the categories have no natural order), but you can sort rows by frequency to identify the mode. For ordinal data (e.g., Likert scale responses), cumulative frequency is meaningful.

Column	What it means	Use for
Frequency (f)	Count of times this value appears	Finding the mode; spotting common values
Relative frequency	f / n — proportion in 0–1 range	Comparing across datasets of different sizes
Relative frequency %	(f / n) × 100	Clear communication of proportions
Cumulative frequency	Running total of f from smallest to current	How many values are at most X
Cumulative %	Running total of relative frequency × 100	Reading percentiles; what % scored ≤ X

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Reading the Frequency Table

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