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.