Calculation of Median | How to Calculate Median in Individual, Discrete & Continuous series – Measures of Central Tendency

Calculation of Median | How to Calculate Median in Individual, Discrete & Continuous series – Measures of Central Tendency for Grouped and Ungrouped Data.

The median is a measure of central tendency that represents the middle value of a dataset. It is calculated by arranging the data in order of magnitude and then selecting the middle value. The median is used when the data is skewed or has outliers.

The formula to calculate the median – measures of central tendency for grouped data is:

Median = l+ [ ((n/2) – cf)/f] × h

Where l = lower limit of median class,

n = number of observations,

h = class size,

f = frequency of median class,

cf = cumulative frequency of class preceding the median class .

For individual data, the formula to calculate the median is:

Median = (n + 1)/2th observation.

For discrete data, the formula to calculate the median is:

Median = Value of [ N +1/ 2] [ N + 1/ 2] th item Where N = Σf.

For continuous data, the formula to calculate the median is:

Median = l + (n 2 − cf) / f × h 

For Explanation, Formula and calculation of median in different series such as individual, discrete and continuous for measures of central tendency , watch the below video

To calculate the median in individual, discrete, and continuous series, you need to follow different methods based on the nature of the data. Let’s go through each type:

1. Individual Series:

   In an median individual series – measures of central tendency, each value is treated as a separate entity without any grouping. To find the median:

   • Arrange the data values in ascending order.
   • If the number of data points (n) is odd, the median is the value at the center of the sorted list.
   • If the number of data points is even, the median is the average of the two middle values.
   •  

2. Discrete Series:

   In a median discrete series – measures of central tendency, data is grouped into different classes or categories, and the frequency of each class is given. To find the median:

   • Calculate the cumulative frequency of each class (the sum of frequencies up to that class).
   • Identify the class or interval where the cumulative frequency becomes equal to or greater than (n/2), where n is the total number of data points.
   • Use the formula: Median = L + [(n/2 – CF) * c] / f
     • L: Lower boundary of the median group
     • CF: Cumulative frequency of the group before the median group
     • c: Width of each class or interval
     • f: Frequency of the median group
     •  

3. Continuous Series:

   In a median in continuous series – measures of central tendency, data is grouped into continuous classes or intervals, and the frequency of each interval is given. To find the median:

   • Calculate the cumulative frequency of each interval (the sum of frequencies up to that interval).
   • Identify the interval where the cumulative frequency becomes equal to or greater than (n/2), where n is the total number of data points.
   • Use the formula: Median = L + [(n/2 – CF) * h] / f
     • L: Lower boundary of the median interval
     • CF: Cumulative frequency of the interval before the median interval
     • h: Width of each interval
     • f: Frequency of the median interval

Note: In continuous series, the median may lie within a particular interval, and you need to interpolate to get an accurate value.

Remember to choose the appropriate method based on the type of data you are working with—individual, discrete, or continuous series—and apply the corresponding formula accordingly.

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