Question bank — Data collection — primary vs secondary, tally charts, frequency tables

$f$ Frequency and $f$ ::: Frequency is the count — how many times a value or category shows up. We write it with the letter $f$. When there are several categories we tag each one with a little number: $f_1$ is the first category's count, $f_2$ the second, and in general $f_i$ means "the count of the $i$-th category" (read $i$ as "which row we're looking at").

$\sum f$ (sigma notation) means $\sum f$ ::: The tall Greek letter $\sum$ (capital "sigma") is a shorthand for "add them all up". So $\sum f=f_1+f_2+f_3+\dots$ means "take every category's frequency and total them". It is just an economical way to say "the grand total of all the counts" without writing out a long $+\cdots +$ chain.

$n$ mean Sample size $n$ ::: The number of observations you actually made — how many people you surveyed, dice you rolled, plants you measured. We call it $n$. Because each observation adds exactly $1$ to exactly one category, the grand total of counts equals the sample size: $\sum f=n$.

Tally ::: A single upright mark ($|$) that stands for one observation, drawn the instant it happens. Four marks stand side by side ($||||$); the fifth mark is drawn diagonally across those four, turning them into a bundle worth $5$. In this note we picture that crossed bundle as "$\overline{||||}$" and refer to it in words as a crossed group of five — that diagonal stroke is the whole convention (see the figure below).

Cumulative frequency ::: A running total of frequencies read from the top of the table downward. The cumulative frequency at row $i$ is $C_i=f_1+f_2+\cdots +f_i={\sum }_{k=1}^i{f}_k$ (add every count from the first row down to row $i$). Because you only ever add non-negative counts, this running total can never shrink as you move down.