how to find cumulative relative frequency

An online relative frequency calculator displays a table that describes how many times given values occur relative to all the observations in the dataset. The frequency distribution calculator also spits out the number of other descriptors of given data. So, if you wonder how exactly it works and displays a frequency distribution table, then dive right in and find out!

What is Relative Frequency?

In mathematics, the relative frequency of events is defined as the ratio of the number of successful tests to the total number of tests performed. Relative frequency is simply the number of times something happened divided by the number of all attempts. The relative frequency distribution must be in the percentage.

Since this is experimental, different relative frequencies can be obtained by repeating the experiment. To calculate the frequency, we need to calculate:

Calculate the frequency of the entire population
Calculate the frequency of a subgroup of the population

Relative Frequency Formula:

Relative frequency is a comparison of the digital repetition frequency and the total frequency of all numbers. From a mathematical point of view, the relative frequency is the individual frequency of the element divided by the total number of repetitions that occur.

The calculation formula of relative frequency distribution is as follows:

Relative Frequency = f / n

Here,

n = total frequencies

f = number of times the data occurred in one observation

However, an online Z Score Calculator allows you to find a z-score from the given raw value. Also, this z value calculator helps to find the z-value by using raw data point, the s ample mean and size, data sample, and 'P' value.

How to Calculate Relative Frequency?

Here's a detailed example of how to find cumulative frequency for successful trials step-by-step:

Example:

How to find relative frequency for the \( 4, 14, 16, 22, 24, 25, 37, 38, 38, 40, 42, 42, 45, 44 \) with 4 number of groups.

Solution:

Firstly, the frequency table maker generates a table according to the given number of groups.

Group	Frequency	Cumulative Frequency	Relative Frequency	Cumulative Relative Frequency
\( 4 – 15 \)	\( 2 \)	\( 2 \)	\( 0.14285714285714 \)	\( 0.14285714285714 \)
\( 16 – 27 \)	\( 4 \)	\( 6 \)	\( 0.28571428571429 \)	\( 0.42857142857143 \)
\( 28 – 39 \)	\( 3 \)	\( 9 \)	\( 0.21428571428571 \)	\( 0.64285714285714 \)
\( 40 – 51 \)	\( 5 \)	\( 14 \)	\( 0.35714285714286 \)	\( 1 \)

Now, the relative frequency calculator provides several statistical characteristics for the given data set such as:

Data Set = \( {4, 14, 16, 22, 24, 25, 37, 38, 38, 40, 42, 42, 45, 44} \)

The cumulative frequency calculator sorted the given data set = \( {4, 14, 16, 22, 24, 25, 37, 38, 38, 40, 42, 42, 44, 45} \)

Mean of frequency distribution: \( μ = 30.785714285714 \)

Median = \( 37.5 \)

Mode = \( {38, 42} – multimodal \)

Minimum = \( 4 \)

Maximum = \( 45 \)

Range =\( 41 \)

Number of Items = \( 14 \)

Sum = \( 431 \)

Sum of Squares = \( 2230.3571428571 \)

Absolute Sum = \( 431 \)

Variance = \( 159.3112244898 \)

Population Standard Deviation \( (σ) = 12.621855033623 \)

Sample Standard Deviation \( (s) = 13.098317986136 \)

Coefficient of Variation \( (Cv) = 0.42546740558214 \)

Signal-to-Noise Ratio \( (SNR) = 2.3503563066876 \)

Geometric Mean =\( 26.589203630878 \)

Harmonic Mean =\( 19.766279777932 \)

Absolute Deviation = \( 159.42857142857 \)

Mean Absolute Deviation = \( 11.387755102041 \)

Quartile Q1 = \( 20.5 \)

Quartile Q2 = \( 37.5 \)

Quartile Q3 =\( 42 \)

Interquartile Range (IQR) = \( 21.5 \)

Quartile Deviation (QD) =\( 10.75 \)

Coefficient of Quartile Deviation (CQD) = \( 0.344 \)

Lower Fence = \( -11.75 \)

Upper Fence = \( 74.25 \)

Z Score = \( {-2.1222, -1.3299, -1.1714, -0.6961, -0.5376, -0.4584, 0.4923, 0.5716, 0.5716, 0.73, 0.8885, 0.8885, 1.0469, 1.1262} \)

Lastly, the relative frequency calculator displays a column chart of Input Values:

Relative Frequency Chart

However, an online Mean Median Mode Range Calculator allows you to calculate the mean median mode and range for the given data set.

Cumulative Relative Frequency:

Cumulative relative frequency is the accumulation of previous relative frequencies. To get this, add all previous relative frequencies to the current relative frequency. The last value is equal to the sum of all observations. Because all the previous frequencies have been added to the previous sum.

How to Calculate Cumulative Frequency?

The cumulative frequency of a value of a variable is the number of values in the collection of data less than or equal to the value of the variable.

Example:

Consider the frequency distribution below.

Class Interval	Frequency
\( 4 – 13 \)	\( 1 \)
\( 14 – 23 \)	\( 3 \)
\( 24 – 33 \)	\( 2 \)
\( 34 – 43 \)	\( 6 \)
\( 44 – 53 \)	\( 2 \)
Total	\( 14 \)

Solution:

The cumulative frequency of 4 – 13 is 1, 14 – 24 is 4, and 24 – 33 is 6, etc.

The above frequency table can generate the following cumulative frequency table.

Class Interval	Frequency	Cumulative Frequency
\( 4 – 13 \)	\( 1 \)	\( 1 \)
\( 14 – 23 \)	\( 3 \)	\( 1 + 3 = 4 \)
\( 24 – 33 \)	\( 2 \)	\( 1 + 3 + 2 = 6 \)
\( 34 – 43 \)	\( 6 \)	\( 1 + 3 + 2 + 6 = 12 \)
\( 44 – 53 \)	\( 2 \)	\( 1 + 3 + 2 + 6 + 2 = 14 \)
Total	14 \)

How does Relative Frequency Calculator Work?

The frequency distribution calculator determines the relative frequency for individuals and groups separately by following these guidelines:

Input:

First, enter the data set for relative frequency distribution, separated with comma (,).
Now, choose the individual or group frequency according to requirements.
Hit the calculate button for relative frequency.

Output:

The frequency table calculator Display:

If you select Individual Frequency, then it shows

Table for cumulative, relative, and cumulative relative frequency for the given data set individually with graph.
It also shows the sorted data set, Mean, Median, Mode, Range, Sum of square, Variance, etc.

If you choose Group Frequency, then the relative frequency calculator provides:

Frequency table with the different number of groups.
Statistical characteristics and column chart for input group values.

FAQ:

What is the difference between relative frequency and absolute frequency?

A relative frequency is the proportion or fraction of times a value occurs in a data set. On the other hand, the cumulative frequency distribution provides subtotals of all the previous frequencies in the frequency distribution.

How to use relative frequency?

Relative frequency can be used to simplify very large values. For example, if you have an experiment with twenty-five successes per hundred trails, it might be easier to set it to a relative frequency of 1/4.

Conclusion:

Use this relative frequency calculator for computing the relative and cumulative frequency of the successive numerical data items either in groups of equal size or individually. Frequency is a measure of how often a specific event occurs. On the other hand, relative frequency is a measure of the frequency of occurrence of a specific event compared to the total number of events.

Reference:

From the source of Wikipedia: Absolute frequency, cumulative frequency, relative frequency, Histograms, Bar graphs, Frequency distribution table.

From the source of Lumen Learning: Frequency & Frequency Tables, Relative frequency, Cumulative relative frequency, percentage of rainfall.

From the source of Study dot com: Frequency & Relative Frequency Tables, Frequency Chosen Number, frequency theory of probability.