Key takeaway: A frequency table lists each possible value or interval of a data set next to the number of times it occurs, which organizes raw data so patterns can be seen.
Grade 66.SP.B.4Statistics and Data
Definition of Frequency Table
A frequency table organizes data by pairing every value with its count. Instead of reading a long list of numbers, you read one row per value: the value, and how many times it showed up. The count is called the frequency.
Tally marks help while collecting: draw one stroke per observation and cross four strokes with a fifth. After counting, replace the tally by a number. Add all frequencies to confirm the total matches the number of observations. Dividing a frequency by the total gives its relative frequency, which can be written as a fraction or a percent. From the table you can draw a dot plot or a bar graph quickly.
Formula and notation
The usual columns are the value, a tally, and the frequency. Relative frequency is
\[\text{relative frequency} = \frac{\text{frequency of a value}}{\text{total number of values}}\]
The frequencies must add up to the total number of observations.
Key facts
- Each row of a frequency table names one value; the number beside it says how often it happened.
- The sum of the frequency column equals the size of the data set.
- Relative frequencies add to 1, or to 100% when written as percents.
- Grouping into intervals keeps a frequency table short when there are many different values.
Frequency Table example
A youth soccer team played 24 games. Goals per game were: 0 goals in 3 games, 1 goal in 6 games, 2 goals in 8 games, 3 goals in 5 games and 4 goals in 2 games. Find the fraction of games with exactly 2 goals and the number of games with at least 3 goals.
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Check the total: \(3 + 6 + 8 + 5 + 2 = 24\).
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Relative frequency of 2 goals: \(\frac{8}{24} = \frac{1}{3}\).
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At least 3 goals means the rows for 3 and 4: \(5 + 2 = 7\) games.
One third of the games had 2 goals, and 7 games had at least 3 goals.
Common mistake
Watch out
Lena adds the values in the goals column, \(0 + 1 + 2 + 3 + 4 = 10\), and says the team played 10 games.
Why it is wrong
The goals column lists possible values, not counts. The number of games is the sum of the frequency column: \(3 + 6 + 8 + 5 + 2 = 24\).
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Statistics and Data