Histogram Median Calculator

Formula

The formula to calculate the median of a histogram is:

$M = L + \left( \frac{N/2 - CF}{F} \right) \times C$

Where:

$M$ is the median of the histogram
$L$ is the lower class boundary of the group containing the median
$N$ is the total number of data points
$CF$ is the cumulative frequency of the group before the median group
$F$ is the frequency of the median group
$C$ is the width of the group interval

What is a Histogram Median?

A histogram median is a value that divides a histogram into two equal areas. It is the middle value of a data set, separating the data into two halves. In a histogram, it is represented by the point at which the area under the curve to the left equals the area under the curve to the right. It is a measure of central tendency that gives a good idea of the central location of the data, especially when the data set is skewed or contains outliers.

Example Calculation

Let's assume the following values:

Lower Class Boundary ( $L$ ): 10
Total Number of Data Points ( $N$ ): 100
Cumulative Frequency Before Median Group ( $CF$ ): 40
Frequency of Median Group ( $F$ ): 20
Width of Group Interval ( $C$ ): 5

Step 1: Calculate the position of the median:

$\frac{N}{2} = \frac{100}{2} = 50$

Step 2: Calculate the median using the formula:

$M = 10 + \left( \frac{50 - 40}{20} \right) \times 5 = 10 + \left( \frac{10}{20} \right) \times 5 = 10 + 0.5 \times 5 = 12.5$

Therefore, the median of the histogram is 12.5.