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Mode of the series of distributing class intervals - calculator

Online calculator calculates the mode of series of distributing class intervals. You learn how to find the Modal value for a grouped data with different intervals between the data classes.

To get the result, enter the intervals separated by "-" eg 10-20 and frequency.

See also:

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Mode, modal values - series of distributing class intervals - calculator

Short information

Mode the most common, modal value is the value (variant) of the feature that occurs most often in the surveyed statistical community. When interpreting the modal one, it should be remembered that it characterizes units with a typical variable level, not all examined units.

The designation of the mode is justified when:

- there are enough observations;

- the empirical size distribution is a unimodal distribution (one dominant center);

- the asymmetry of the abundance distribution is moderate;

- class intervals with mode and two adjacent intervals have the same length;

- mode can be designated on open interval distribution series (e.g. less than 5 years, more than 65 years);

- its value is not affected by the extreme values of the series (x min and x max);
Mode is not determined when the distribution series is bimodal or multimodal.

EXAMPLE

In one of the companies, the distance between the employees' place of residence and the workplace was examined, the data was as follows:

Distance of residence in km. $ (x_{0i}+x_{1i})$	Number of employees $(f_i) $
0-5	5
5-10	25
10-15	30
15-20	55
20-35	25
25-30	20
30-35	15

The task is to calculate the mode of the given distribution series.

First, let's define the statistical population, statistical unit and variable.
The statistical population is made up of employees. The statistical unit is one employee. A feature of a continuous quantitative variable is the distance to work from the place of residence.

From the first row of the data table, we read that 5 employees travel from 0 to 5 kilometers to work. The second row shows that 25 workers live between 5 to 10 km from work, etc.

Mode is the value of the dominant variable feature that occurs most often. In the example above, the variable feature is the distance between home and work.

The table shows that most employees live within 15 to 20 km. Therefore, the 15-20 range is the mode range and the number of employees (55) is the frequency of the modal range.

Thanks to the formula for the mode of the interval distribution series, we can calculate the most frequent distance between employees' residence and the workplace.

$$ M_0=x_0+\frac{f_0-f_{-1}}{(f_0-f_{-1})+(f_0-f_{+1})}\cdot h_0 $$

f₀ = 55 - frequency of the modal range (highest frequency)
15-20 - modal range;
x₀ = 15 - lower class boundary of the modal range
f_-1 = 30 - frequency of the range before the modal range (frequency from a row above frequency of the modal range 55)
f₊₁ = 25 - the frequency of the range after the modal range (frequency from a row below frequency of the modal range 55)
h₀ = x_1M(higher) - x_0M(lower) = 20 - 15 = 5 - size (width) of the modal range (difference between the higher value of the modal range and its lower value)

Substituting the above into the formula we can calculate mode.

$$ M_0=15+\frac{55-30}{(55-30)+(55-25)}\cdot 5 $$ $$ M_0=17,27 $$

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