The cumulative frequency is the acquired result of the continuous sum of the absolute or relative frequencies when performed from lowest to highest, depending on the values they understand, that is, it refers to the number of times that a certain event repeats a sample.
The number of repetitions is known as the absolute frequency, in case this is divided by the size of the sample, the result obtained is called the relative frequency. The result of these data is when the calculation of the cumulative frequency.
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In this article you will find:
Cumulative frequency examples
This type of frequency adds all the values lower than or equal to the value considered and is represented by the letter F. Here are some cumulative frequency examples:
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Example 1
Find out if a certain group of people is for or against programming with violent messages on television, through the collection of the following data:
X: 2, 1, 5, 3, 3, 2, 3, 1, 4, 2, 4, 2, 3, 2, 3, 4, 3, 3, 1, 2
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Coding standard:
- 1: Against
- 2: Totally against
- 3: Indifferent
- 4: Totally in favor
- 5: In favor
The investigation of the original data does not provide answers related to the attitude of the majority of the group, which makes it difficult to determine the level of attitude difference between men and women. This could be improved if used in a table of values, the variables next to the number of times or frequency that each value appears:
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| X | F |
| 1 | 3 |
| 2 | 6 |
| 3 | 7 |
| 5 | 3 |
| 4 | 1 |
| Total | 20 |
- X: It is the symbol of the variable.
- F: Represents the frequency.
In this example, the frequency distribution of data has shown that most of the people in the group are indifferent. Interpretation of data improved as the number of numbers examined decreased.
Example 2
This example shows the number of absolute frequencies, in order to totalize the events that are ordered in a list, which are equal to or less than the value determined.
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Approach: Assume the grades of 20 students.
1, 2, 8, 5, 8, 3, 8, 5, 6, 10, 5, 7, 9, 4, 10, 2, 7, 6, 5, 10
To begin, it has to be done to find the accumulated absolute frequency, it is to organize the data from smallest to largest and then tabulate and accumulate, to obtain the following results:
- Xi: Random statistical variable, exam grade.
- Fi: Number of times the exam grade is repeated.
- N: 20
It is essential that the totality of the absolute frequency coincides with the total of the sample so that it is demonstrated that the accumulated verification is the corresponding one.
Example 4
In this last example, the approach is as follows: during the month of April, the following maximum temperatures were recorded in a specific place:
32, 31, 28, 29, 33, 32, 31, 30, 31, 31, 27, 28, 29, 30, 32, 31, 31, 30, 30, 29, 29, 30, 30, 31, 34, 33, 33, 29, 29
- The first column of the table must contain the variable ordered from least to greatest.
- The second column has the annotations of the absolute frequency.
- The third column contains the annotations of the accumulated frequency.
- The first box corresponds to the first absolute frequency Fi = f.
- In the second box, the sum of the value of the previous accumulated frequency is performed together with the appropriate absolute frequency Fi + fi = 1 + 2 = 3.
- In the third box, the value of the previous accumulated frequency is added with the absolute frequency that is appropriate Fi + fi = 3 + 6 = 9.
- The final box must be equal to N: Fi = N = 31.
- The fourth column contains the relative frequencies (ni), which would be the result of dividing the absolute frequencies and N (31).
- The fifth column records the accumulated relative frequency Ni.
- The first accumulated relative frequency is placed in the first box.
- In the second box, the value of the previous accumulated relative frequency is added together with the appropriate relative frequency and it is continued until reaching the last one, which must be equal to 1.
| X | fi | Fi | neither | Neither |
| 27 | 1 | 1 | 0.032 | 0.032 |
| 28 | 2 | 3 | 0.065 | 0.097 |
| 29 | 6 | 9 | 0.194 | 0.290 |
| 30 | 7 | 16 | 0.226 | 0.516 |
| 31 | 8 | 24 | 0.258 | 0.774 |
| 32 | 3 | 27 | 0.097 | 0.871 |
| 33 | 3 | 30 | 0.097 | 0.968 |
| 34 | 1 | 31 | 0.032 | 1 |
| 31 | 1 |
These cumulative frequency examples, show that a result can be obtained from the successive summation of the absolute or relative frequencies, from the lowest to the highest of their corresponding values.
