Median & Range ---> Mean & Standard Deviation (SD)
Introduction
Median: The median is a measure of central tendency that represents the middle value in a dataset when it is ordered from least to greatest. In other words, it is the value that separates the higher half from the lower half of the data. Unlike the mean (average), the median is not influenced by extreme values, making it a robust measure in the presence of outliers. To determine the median, you arrange the data in ascending order and identify the middle value. If there is an even number of observations, the median is the average of the two middle values.
Range: The range is a measure of the spread or dispersion of a dataset and represents the difference between the maximum and minimum values. It provides a simple indication of how much the values in a dataset vary. A larger range suggests greater variability, while a smaller range indicates less variability. To calculate the range, subtract the minimum value from the maximum value. While the range is easy to compute, it can be sensitive to outliers and may not fully capture the distribution's characteristics.
Maximum: The maximum is the highest value in a dataset. It represents the upper limit or the largest observation in the dataset. Identifying the maximum value is useful for understanding the extreme values within the data. In some contexts, such as quality control or outlier detection, monitoring and analyzing the maximum value can be essential for ensuring data quality or identifying unusual patterns.
Minimum: The minimum is the lowest value in a dataset, representing the lower limit or the smallest observation. Similar to the maximum, identifying the minimum value is crucial for understanding the range of values present in the data. The minimum value is often used to establish a baseline or reference point, and it can be important in various statistical analyses and decision-making processes.
Mean (Average): The mean, also known as the average, is a measure of central tendency that represents the arithmetic average of a set of values. It is calculated by adding up all the values in a dataset and dividing the sum by the number of observations. The mean provides a measure of the "typical" or "central" value in a dataset. It is widely used in various fields, and it is particularly sensitive to extreme values (outliers) in the dataset.
Standard Deviation (SD): The standard deviation is a measure of the dispersion or spread of a dataset. It quantifies how much individual values in a dataset deviate from the mean. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation suggests that the values are more spread out. The standard deviation is calculated by taking the square root of the variance.
In meta-analyses, researchers often encounter situations where they need to estimate the mean and standard deviation of a dataset based on limited information, such as the median and range. This article introduces a conversion tool designed to calculate the mean and standard deviation from the median and range, providing a practical solution for researchers and analysts working with incomplete data.
Variables Definitions
Median: The middle value of a dataset, separating it into two equal halves.
Minimum: The smallest value in the dataset.
Maximum: The largest value in the dataset.
Sample Size: The number of observations or data points in the dataset.
Mean: The calculated average of the dataset.
Standard Deviation: A measure of the dispersion or spread of the dataset.
Conversion Formula
The standard deviation is calculated using the Wan et al. method:
