Calculate the median for data with class interval with this free median calculator. Just enter the class and their frequency in each row, and the cumulative frequency will be calculated automatically. Please be correct when entering your statistical data to avoid any errors.
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What is the Median in Statistics?
The median is a measure of central tendency that is used to find out the middle value of a dataset or a population table that has been ordered from smallest to largest value or vice versa.
In statistics, the mean can be affected by the extreme values or outliers in a dataset. While the median focuses on the middle position and remains stable even with the presence of outliers.
Let’s see the importance of the median with a simple example.
Suppose the household incomes in a small town: $25,000, $30,000, $35,000, $40,000, $45,000, and $1,000,000. The mean income is $195,833, which is not representative of most people’s income. The median income is $37,500, which gives a much better idea of the typical income in that town.
Median with an odd number of data counts
If the data count is odd in an unclassified dataset, we use the formula (n + 1)/2th number of value in the dataset to calculate the median. Here’s an example:
Consider the dataset: 20, 50, 10, 80, 30
- Order the data: 10, 20, 30, 50, 80
- The number of data counts is 5 (odd).
- The position of the median is (5+1)/2 = 3.
- The 3rd value in the ordered dataset is 30. Therefore, the median is 30.
- Median with an even number of data counts
Median with an even number of data counts
We use the formula, [(n/2)th value + {(n/2)+1}th value] / 2 to calculate the median with an even number of data points.
Consider the dataset: 40, 90, 20, 70, 10, 50
- Order the data: 10, 20, 40, 50, 70, 90
- The number of data counts (n) is 6 (even).
- Apply the formula; 6/2 is 3, and (6/2) + 1 is 4.
- The 3rd value is 40, and the 4th value is 50.
- The median is the average of these two values: (40+50)/2. Therefore, the median is 45.
Three main characteristics of median
- Resist the outliers: Unlike the mean (average), the median is not significantly affected by extreme values (outliers) in the dataset. This makes it a more robust measure of central tendency when dealing with skewed distributions or data containing outliers.
- Positional measure: The median is based on the position of the data points in the ordered dataset.
- Divides the data: The median divides the dataset into two halves, with 50% of the data falling below it and 50% above it.
That’s all for today. If you determine anything is wrong with this median calculator, please drop your valuable feedback in the comment section below.