Frequency Distribution Calculator

This frequency distribution calculator is used to organize and summarize data by grouping values into categories and counting their occurrences. This method provides a clear picture of how often different values or ranges appear within a dataset.

For example, imagine you’re analyzing the ages of students in a university:

Ages: 18, 19, 20, 18, 21, 19, 20, 22, 18, 20, 19, 21, 18, 20, 19

Age	Frequency
18	4
19	4
20	4
21	2
22	1

This representation table quickly reveals that ages 18, 19, and 20 are the most common, each occurring four times.

Frequency Distribution Calculator

Grades: A, B, C, A, B, D, C, B, A, F, C, B, A, C, B, A, D, C, B, A

Grade	Frequency	Relative Frequency	Cumulative Frequency
A	6	0.30	0.30
B	6	0.30	0.60
C	5	0.25	0.85
D	2	0.10	0.95
F	1	0.05	1.00

From this table, we can derive several insights:

• The mode (most frequent grade) is tied between A and B.
• 60% of students received a grade of B or higher.
• Only 5% of students failed the course.
• The median grade falls in the B category (as the 50th percentile is at 0.60).

Frequency Distribution Formula

Frequency = Number of occurrences of a value / Total number of values

Let’s examine a more complex example using test scores:

Scores: 65, 70, 75, 80, 85, 90, 95, 65, 70, 75, 80, 85, 90, 95, 70, 75, 80, 85, 90, 95

We can group these scores into intervals:

Score Range	Frequency	Relative Frequency
60-69	2	0.10
70-79	5	0.25
80-89	6	0.30
90-99	7	0.35

The relative frequency is calculated by dividing each frequency by the total number of scores (20 in this case).

How do I calculate frequency distribution?

1. Collect and organize data: Gather your dataset and arrange it in ascending order.
2. Determine categories or intervals: For continuous data, decide on appropriate intervals.
3. Count occurrences: Tally how many times each value or interval appears.
4. Calculate frequencies: Divide the count by the total number of observations.
5. Create a table or graph: Present your results in a clear, visual format.

Let’s walk through an example using daily temperatures for a week:

Temperatures (°F): 72, 75, 68, 70, 73, 71, 69

1. Organize the data: 68, 69, 70, 71, 72, 73, 75
2. Count occurrences:
   • 68: 1
   • 69: 1
   • 70: 1
   • 71: 1
   • 72: 1
   • 73: 1
   • 75: 1
3. Calculate frequencies (divide by 7):
   • 68: 1/7 ≈ 0.14
   • 69: 1/7 ≈ 0.14
   • 70: 1/7 ≈ 0.14
   • 71: 1/7 ≈ 0.14
   • 72: 1/7 ≈ 0.14
   • 73: 1/7 ≈ 0.14
   • 75: 1/7 ≈ 0.14

Temperature (°F)	Frequency	Relative Frequency
68	1	0.14
69	1	0.14
70	1	0.14
71	1	0.14
72	1	0.14
73	1	0.14
75	1	0.14

This distribution shows an even spread of temperatures throughout the week.

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