Frequency
Statistics & ProbabilityFrequency is the number of times a particular value or category appears in a dataset.
Definition
Frequency is how many times something appears or happens in a set of data. It is a simple count.
Example
If $8$ students chose "pizza" as their favorite food and $5$ chose "tacos," the frequency of pizza is $8$ and the frequency of tacos is $5$.
Key Insight
Counting frequencies is the first step in organizing data. It turns a messy list into useful summary information.
Definition
Frequency is the count of how many times each value or category occurs in a dataset. Frequencies can be organized into a frequency table and displayed with bar graphs (for categorical data) or histograms (for grouped numerical data).
Example
Test scores: $72$, $85$, $91$, $85$, $72$, $78$, $91$, $91$. Frequency of $91$ is $3$; frequency of $85$ is $2$; frequency of $72$ is $2$; frequency of $78$ is $1$.
Key Insight
Frequency tells you about distribution shape: where values cluster and where they are rare. Comparing frequencies across groups can reveal important patterns.
Definition
Frequency is the observed count $n_i$ for the i-th category or class interval, with total $n = \sum n_i$. The frequency distribution is a complete specification of all $n_i$ values. For continuous data, class intervals are used, and the histogram approximates the underlying probability density function.
Example
As class interval width $h \to 0$ and $n \to \infty$, the normalized histogram (frequency density $= n_i/(nh)$) converges to the true PDF $f(x)$, a principle underlying kernel density estimation.
Key Insight
Kernel density estimation (KDE) smooths the histogram by replacing each observation with a smooth kernel function (e.g., Gaussian), producing a continuous PDF estimate whose properties depend on the bandwidth parameter.