Frequency
Frequency 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, a simple count of how many times each value or category occurs. Frequencies can be organized into a frequency table and displayed with bar graphs (for categorical data) or histograms (for grouped numerical data). Formally, 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, and for continuous data, class intervals are used, with the histogram approximating the underlying probability density function.
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 $5$. For test scores $72$, $85$, $91$, $85$, $72$, $78$, $91$, $91$: the frequency of $91$ is $3$, of $85$ is $2$, of $72$ is $2$, and of $78$ is $1$. 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
Counting frequencies is the first step in organizing data, turning a messy list into useful summary information that reveals distribution shape: where values cluster and where they are rare. 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.