Frequency and Tally

Frequency and Tally

What is it?

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.

In simple words

• Frequency f is the count of values in a class (or the count of a single number in ungrouped data).
• Checks you should run before you trust a table:
• frequency f: how many values in that class.
• cumulative frequency CF: running total of f down the table.

Important terms

Frequency: Frequency f is the count of values in a class (or the count of a single number in ungrouped data).

count: Frequency f is the count of values in a class (or the count of a single number in ungrouped data).

Cumulative frequency: Cumulative frequency CF is the running total of frequencies from the first class down to this row.

running total: Cumulative frequency CF is the running total of frequencies from the first class down to this row.

last CF = n: The last CF = n, the number of observations.

What you should learn

• Explain frequency and tally in clear mathematical language.
• Use the main rule, formula, test, or construction correctly.
• Work through a simple example and show each important step.
• Identify common mistakes and write an exam-ready conclusion.

Full school-level explanation

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.

WHAT — Core idea

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.

HOW — Rules, method, and examples

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.

WHY — Meaning and connections

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.

HOW — Answer in an exam

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.

Remember

• Frequency
• count
• Cumulative frequency
• running total
• last CF = n
• 5-15
• h ~ xl-xsk
• fifth mark diagonal

How the ideas connect

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.

Deeper understanding

Go beyond memorising Frequency and Tally. Connect the definition to reasons, relationships, exceptions, and exam wording.

How the ideas connect

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.

Common mistakes

Exam focus

WHAT

Key Points

HOW

Examples

Exam focus

Quick revision

• Frequency
• count
• Cumulative frequency
• running total
• Frequency: Frequency f is the count of values in a class (or the count of a single number in ungrouped data).
• count: Frequency f is the count of values in a class (or the count of a single number in ungrouped data).

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.

For long answers on Frequency and Tally: define clearly → explain the main parts → give one example → state one exam caution.