Mean median Mode for Frequency Distribution Calculator

The mean of frequency distribution referred to as the average. For frequency distributions, where data is grouped into intervals with corresponding frequencies, calculating the mean can be complex.

The median of grouped data reprensents the middle value of a dataset. In the case of grouped data or frequency distributions, finding the median manually involves calculations.

The mode of frequency distribution reprensets the value that appears most frequently in a dataset. In frequency distributions, finding the mode can be challenging due to the grouped nature of the data.

However, using the below Mean of frequency distribution calculator, you can input the frequency distribution data, and the calculator will compute the mean, median and mode of the grouped data.

Mean of Frequency Distribution Calculator
Type of Frequency Distribution DiscreteContinuous
Enter the Classes for X (Separated by comma,)
Enter the frequencies (f) (Separated by comma,)
Mean of Frequency Distribution - Results
Number of Obervations. (N):
Mean of Frequency Distribution:
Median of Grouped Data:
Mode of Frequency:
Frequency distribution :

How to use Mean of frequency distribution calculator?

  • Select type of frequency distribution either Discrete or continuous

  • Enter the Range or classes (X) seperated by comma (,)

  • Enter the Frequencies (f) seperated by comma

  • Click on Calculate for mean,mode and median of grouped data

  • Gives output as number of observation (n)

  • Calculate mean of frequency distribution

  • Calculate mode of frequency distribution

  • Calculate median of frequency distribution

Mean, mode and median of grouped data

Let $x_1, x_2, \cdots , x_n$ have frequencies $f_1, f_2, \cdots ,f_n$ respectively, then the Harmonic Mean is given by

$$ \begin{equation*} Mean =\overline{X} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i\quad \mbox{ where }N = \sum_{i=1}^{n} f_i \end{equation*} $$

In case of continuous frequency distribution, $x_i$’s are the mid-values of the respective classes.

Mean median mode for grouped data formula

Sample mean

The mean of $X$ is denoted by $\overline{x}$ and is given by

$\overline{x} =\dfrac{1}{N}\sum_{i=1}^{n}f_ix_i$

In case of continuous frequency distribution, $x_i$’s are the mid-values of the respective classes.

Sample median

The median of frequency distribution is given by

$\text{Median } = l + \bigg(\dfrac{\frac{N}{2} - F_<}{f}\bigg)\times h$

where

  • $N$, total number of observations
  • $l$, the lower limit of the median class
  • $f$, frequency of the median class
  • $F_<$, cumulative frequency of the pre median class
  • $h$, the class width

Sample mode

The mode of the frequency distribution is given by

$\text{Mode } = l + \bigg(\dfrac{f_m - f_1}{2f_m-f_1-f_2}\bigg)\times h$

where

  • $l$, the lower limit of the modal class
  • $f_m$, frequency of the modal class
  • $f_1$, frequency of the class pre-modal class
  • $f_2$, frequency of the class post-modal class
  • $h$, the class width

Mean of Frequency Distribution Calculation

The following table gives the amount of time (in minutes) spent on the internet each evening by a group of 56 students. Calculate mean of frequency distribution,median of group data and mode of frequency table for the following frequency distribution.

Time spent on Internet ($x$) 10-12 13-15 16-18 19-21 22-24
No. of students ($f$) 3 12 15 24 2

Solution

The classes are inclusive. To make them exclusive type subtract 0.5 from the lower limit and add 0.5 to the upper limit of each class.

Class Interval Class Boundries mid-value (x) Freq (f) f*x cf
10-12 9.5-12.5 11 3 33 3
13-15 12.5-15.5 14 12 168 15
16-18 15.5-18.5 17 15 255 30
19-21 18.5-21.5 20 24 480 54
22-24 21.5-24.5 23 2 46 56
Total 56 982

Mean

The mean time spent on internet is

$$ \begin{aligned} \overline{x} &=\frac{1}{N}\sum_{i=1}^n f_ix_i\\ &=\frac{982}{56}\\ &=17.5357 \text{ minutes} \end{aligned} $$

Median

Median time spent on internet by the students is $$ \begin{aligned} \text{Median} &=\bigg(\dfrac{N}{2}\bigg)^{th}\text{ value}\\ &= \bigg(\dfrac{56}{2}\bigg)^{th}\text{ value}\\ &=\big(28\big)^{th}\text{ value} \end{aligned} $$ The cumulative frequency just greater than or equal to $28$ is $30$. The corresponding class $15.5-18.5$ is the median class.

Thus

  • $N=56$, total number of observations
  • $l = 15.5$, the lower limit of the median class
  • $f =15$, frequency of the median class
  • $F_< = 15$, cumulative frequency of the pre median class
  • $h =3$, the class width

The median of given frequency distribution can be computed as follows:

$$ \begin{aligned} \text{Median } &= l + \bigg(\frac{\frac{N}{2} - F_<}{f}\bigg)\times h\\ &= 15.5 + \bigg(\frac{\frac{56}{2} - 15}{15}\bigg)\times 3\\ &= 15.5 + \bigg(\frac{28 - 15}{15}\bigg)\times 3\\ &= 15.5 + \big(0.8667\big)\times 3\\ &= 15.5 + 2.6\\ &= 18.1 \text{ minutes} \end{aligned} $$

Mode

The maximum frequency is $24$, the corresponding class $18.5-21.5$ is the modal class.

Mode of the given frequency distribution is: $$ \begin{aligned} \text{Mode } &= l + \bigg(\frac{f_m - f_1}{2f_m-f_1-f_2}\bigg)\times h\\ \end{aligned} $$ where,

  • $l = 18.5$, the lower limit of the modal class
  • $f_m =24$, frequency of the modal class
  • $f_1 = 15$, frequency of the pre-modal class
  • $f_2 = 2$, frequency of the post-modal class
  • $h =3$, the class width

Thus mode of a frequency distribution is

$$ \begin{aligned} \text{Mode } &= l + \bigg(\frac{f_m - f_1}{2f_m-f_1-f_2}\bigg)\times h\\ &= 18.5 + \bigg(\frac{24 - 15}{2\times24 - 15 - 2}\bigg)\times 3\\ &= 18.5 + \bigg(\frac{9}{31}\bigg)\times 3\\ &= 18.5 + \big(0.2903\big)\times 3\\ &= 18.5 + \big(0.871\big)\\ &= 19.371 \text{ minutes} \end{aligned} $$

Conclusion

Hope you like Mean Mode Median for frequency distribution calculator. Click on Theory button to read more about mean median,sample for grouped data and step by step examples explained.

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