Frequency and Tally

Frequency f is the count of values in a class (or the count of a single number in ungrouped data). Cumulative frequency CF is the running total of frequencies from the first class down to this row. The last CF = n, the number of observations. Tally marks are the stick method of counting: four uprights and a fifth mark diagonal through them, so groups of five are easy to add. Plan about 5-15 classes. A rough class size is h ~ xl-xsk, where xl is the largest value, xs the smallest, and k the chosen number of classes.

Checks you should run before you trust a table: frequency f: how many values in that class; Sigma f must equal n. cumulative frequency CF: running total of f down the table; last CF = n. tally: sticks in fives, fifth mark diagonal; count the fives, then convert to f. number of classes k: about 5 to 15 classes; too few hides shape; too many is noisy. discrete width 1: classes like 0, 1, 2, 3 (single values); no boundary column needed.

Always check Sigma f = n after you fill frequencies. If the last CF is not n, a row was dropped or added twice. Discrete data with class width 1 (number of siblings, number of goals) needs no boundary column because there is no gap to close. Continuous grouped marks still need boundaries for a histogram. Choose k first, then h ~ xl-xsk, then round h to a convenient number such as 5 or 10.

Frequency is a count. CF is a running total; last CF = n. Tally in fives with the fifth mark diagonal. Use about 5-15 classes and h ~ xl-xsk. Check Sigma f = n. Discrete width-1 tables need no boundary column.