Mean median Mode for Frequency Distribution Calculator
Use Mean median mode for frequency distribution calculator to find the mean of frequency distribution, median of grouped data and mode of frequency distribution data.
Mean median Mode Calculator (Grouped Data) | |
---|---|
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 mode and median of frequency distribution calculator?
Step 1 - Select type of frequency distribution either Discrete or continuous
Step 2 - Enter the Range or classes (X) seperated by comma (,)
Step 3 - Enter the Frequencies (f) seperated by comma
Step 4 - Click on Calculate for mean,mode and median of grouped data
Step 5 - Gives output as number of observation (n)
Step 6 - Calculate mean of frequency distribution
Step 7 - Calculate mode of frequency distribution
Step 8 - 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
Example -1 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.
Read more about other Statistics Calculator on below links
- Descriptive Statistics Calculators
- Hypothesis Testing Calculators
- Probability Distribution
- Confidence Interval Calculators
- Correlation Regression Calculators
- Probability Theory Calculators
- Sample Size and Power Calculators