Median: Formula, Relation Between Mean, Mode and Median

The gathering, analysis, interpretation, and presentation of large amounts of numerical data are referred to as statistics. Because of his investigations on birth and death data, Captain John Graunt of London is renowned as the “Father of Vital Statistics.” One of the most significant issues in statistics is the median. The median is a measure of central tendency that represents the value of the data’s middle observation. We’ll look at how to find the median for both grouped and ungrouped data in this post.

The median is the number in the middle of an ascending or descending number series, and it may be more descriptive of the data set than the average. When there are outliers in the series that could affect the average of the numbers, the median is sometimes utilized instead of the mean.

Keyterms: Median, Mean, ascending number series, descending number series, data set, average, numbers, central tendency, cumulative frequency

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What is Median?

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The median is the middle number in an ascending or descending sequence of numbers, and it may be more descriptive of the data set than the average. A median is a form of average that is used to locate the center value in mathematics. As a result, it’s also known as a measure of central tendency.

The median of 3, 3, 5, 9, 11 is 5, for example. When there is an even number of observations, the median is commonly defined as the average of the two middle values: for example, the median of 3, 5, 7, 9 is (5+7)/2 = 6.

The median is the (n+1)/2 th observation if n is odd. However, finding the (n+1)/2 th observation in grouped data is difficult. To find the median, we utilize a formula.

We identify the class whose cumulative frequency is greater than (and closest to) n/2, where n is the total number of observations, and then we find the class whose cumulative frequency is bigger than (and closest to) n/2. This is referred to as the median class.

Mean, Median and Mode Video Explanation

Also Read:  Measures of Dispersion

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The formula for Calculating Median

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Here is the formula for calculating the median of a finite number of data sets. For even and odd numbers of observations, the median formula is different. As a result, we must first determine whether we have an odd or even number of values in a given data set. The formula for calculating the data set’s median is as follows.

Odd number of observation

The total number of observations is odd

To calculate the mean we use the below formula:

Median = {(n+1)/2}th term

where n is the number of observation.

Even number of observation

If there are an even number of observations, the median formula is:

Median = [(n/2)th term + {(n/2)+1}th]/2

Where n is the number of observations.

The Mean, Median, and Mode in Relationship

Also Read:  Frequency Distribution Table Statistics

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Relation Between Mean, Mode, and Median

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With the use of his Formula, Karl Pearson illustrates the link between mean, median, and mode as follows:

(Mean – Median) = 1(3)

 (Mean – Mode)

3(Mean – Median) = (Mean – Mode)

Mode = Mean – 3 (Mean – Median)

Mode = 3 Median – 2 Mean

As a result, if you have one of the two numbers and need to find the third, you can use the equation above.

Median of grouped data

We can't merely pick the median number because the data is divided into class intervals. As a result, we'll need to take the following steps:

Step 1: First, we must create a three-column table.

Step 2: In column 1, write the class intervals.

Step 3: In column 2, write the corresponding frequencies marked by fi.

Step 4: In column 3, write the calculated Cumulative Frequency, represented by cf.

Step 5: In this step, we must compute N/2 and obtain the amount of fi represented by N.

Also Read:

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Things to Remember

• The median of a dataset is not determined by all of the data values.
• The median value is determined by its location rather than by the individual value.
• The gap between the median and the remaining values is shorter than the distance between any other position.
• There is only one median in each array.
• Algebraically, the median cannot be changed. It is impossible to weigh and blend it.
• The median remains constant during a grouping procedure.
• In qualitative data, the median does not apply.
• For computation, the values must be grouped and arranged.
• For ratio, interval, and ordinal scales, the median can be calculated.
• Outliers and distorted data have less of an impact on the median.
• The median is a better measure than the mean when the distribution is skewed.

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