How to Find Mean if Median is Given?

To find the mean when the median is given, add the median to the sum of deviations from the median divided by the number of data points.

If you know the median of a dataset and the distribution is assumed to be symmetrical, you can find the mean by setting the mean equal to the median. Here’s a more detailed explanation:

How to Calculate Mean from Median?

1. Assume Symmetry:
   • This method assumes that the dataset is symmetrical. For a symmetrical distribution, the mean and median are equal.
2. Set Mean Equal to Median:
   • In a symmetrical distribution, the mean (μ) is the same as the median (x).
     μ = x
   • For example, in a perfectly symmetrical distribution like a normal distribution, the mean is located at the center, which coincides with the median.
3. Use the Known Median:
   • If you are given the median value x, that value becomes the mean (μ).
     μ = x

Example: If the dataset is symmetrical (e.g., normally distributed) with median x=15, you can set the mean (μ) equal to the median.

μ = x = 15

So, in this case, the mean of the dataset is 15.

This approach simplifies finding the mean when the median is known, but it relies on the assumption of symmetry in the data distribution. If the distribution is skewed, additional information or statistical techniques may be required to estimate the mean accurately.