Mean, Median and Mode of Grouped Data

A comparison between Mean, Median and Mode of Grouped Data has been discussed in the table below:

Mean	Median	Mode
Mean is the average value of all the data points in a given dataset.	Median is the value of middlemost data point when the given dataset is arranged in ascending order.	Mode is the most frequent data point in a dataset.
Formula to find mean of grouped data: Mean = ∑(f_i.x_i)/∑f_i Where, x_i is the mean of upper limit and lower limit of i^thclass interval. f_i is the frequency of the i^th class interval.	Formula to find median of grouped data: Median = l + ((n/2-cf)/f)×h Where, l is the lower limit of median class. h is class size. f is frequency of median class, cf is the cumulative frequency of the class preceding the median class. N = ∑f_i	Formula to find mode of grouped data: Mode = x_k + h{(f_k – f_k-1)/(2f_k – f_k-1 – f_k+1)} Where, x_k is lower limit of the modal class. f_k is frequency of the modal class. f_k-1is the frequency of the class preceding the modal class. f_k+1 is the frequency of the class succeeding the modal class. h is class size.

Mean

Median

Mode

Mean is the average value of all the data points in a given dataset.

Median is the value of middlemost data point when the given dataset is arranged in ascending order.

Mode is the most frequent data point in a dataset.

Formula to find mean of grouped data:

Mean = ∑(f_i.x_i)/∑f_i

Where,

x_i is the mean of upper limit and lower limit of i^thclass interval.
f_i is the frequency of the i^th class interval.

Formula to find median of grouped data:

Median = l + ((n/2-cf)/f)×h

Where,

l is the lower limit of median class.
h is class size.
f is frequency of median class,
cf is the cumulative frequency of the class preceding the median class.
N = ∑f_i

Formula to find mode of grouped data:

Mode = x_k + h{(f_k – f_k-1)/(2f_k – f_k-1 – f_k+1)}

Where,

x_k is lower limit of the modal class.
f_k is frequency of the modal class.
f_k-1is the frequency of the class preceding the modal class.
f_k+1 is the frequency of the class succeeding the modal class.
h is class size.

Also,Check

Mean, Median and Mode of Grouped Data

Mean of Grouped Data

Frequency Distribution

Median of Grouped Data

Median of Grouped Data is the value of the middlemost data point in any dataset when dataset is grouped. For ungrouped data, it is easy to find the median but finding the Median of Grouped Data is slightly complex. When we have any data in statistics, we try to find some basic parameters related to it which provide ease in data interpretation and making further predictions related to data. To measure the central tendency of data, i.e., a single value that can be used to represent an entire distribution, we generally have three parameters: mean, median, and mode.

In this article, we will discuss what is meant by Grouped Data and Median of Grouped Data. We will also learn about the Formula for Median of Grouped Data and steps to calculate the Median of Grouped Data, solved examples, and some frequently asked questions as well.

Table of Content

What is Grouped Data?
What is Median of Grouped Data?
Median of Grouped Data Formula
How to Calculate Median of Grouped Data?
Mean, Median and Mode of Grouped Data

Mean, Median and Mode of Grouped Data

Median of Grouped Data

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Mean, Median and Mode of Grouped Data

Median of Grouped Data

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