Estimating the Median of a histogram

A histogram is a statistical graph that represents the frequency of data values.
It is made of rectangles; the area of each rectangle reflects the frequency of the corresponding data.
The median is the middle value in a set of data when it’s sorted in numerical order.
When observing a histogram, the median divides it into two equal areas.

To estimate the median, first determine the total frequency, or the number of data values.
The median class is the class interval wherein the median lies.
This is found by adding 1 to the total frequency and then dividing by 2.
Scan the cumulative frequency column from top to bottom to find the first value that is larger than half of the total frequency. The corresponding class interval is the median class.
The width, height, and frequency of the bars of the histogram all contribute to calculating the median.

Establish the lower class boundary of the median class.
Identify the cumulative frequency of the class right before the median class.
Determine the class width of the median class.
Identify the frequency of the median class.
Apply the following formula: Median = Lower class boundary + [ ( (N/2) - Cumulative frequency ) / Frequency ] x Class width

Clear comprehension of histograms and how they represent data is crucial.
Always understand that the median class is where the median falls, and it splits the area of histogram in two equal halves.
Thoroughly understand each component of the formula for calculating the median, including the lower class boundary, cumulative frequency, class width, and the frequency of the median class.
The more confident you become with reading histograms, and using the formula for estimating the median, the quicker and more accurately you’ll be able to work with this concept.
Revision and practice remain a key element to master the topic, in addition to interpreting the median and other statistical data on a histogram. Make a habit of solving and revising problems based on this concept.