MEAN vs. MEDIAN
Mean & Median is one of the most innate parts of statistical mathematics. The branch deals with assembly & analysis of data in different and diverse ways for intended calculation. Mean along with median serve these purposes distinctly.
What is Mean & Median?
Mean is stated as an average of some numbers. In simple terms, the mean is the most probable result of the combination of given data. Median states the middle-most data set sorted in specific ways with an equal number of higher and smaller numbers or data.
One of the significant differences between mean vs. median is outliers; it has no impact on the median but may have a considerable effect on the mean number. When calculating the mean, each of the numbers affects the final number whereas outliers will have a minimum or no impact on the final numbers
How To Calculate Mean?
Steps required to calculate the Mean
Step 1: Add all the quantities to get a total number
Step 2: Count the number in a series
Step 3: Now, divide the total found in Step 1 by the number of Step 2.
You will be able to find the mean of quantities and numbers by following the above steps.
In Microsoft Excel, you can also use the formula =AVERAGE(N1, N2, N3……)
Three kinds of Mean explained below:
- Arithmetic Mean: – It is calculated as the sum of the terms divided by the number of terms.
- For a, b, c being terms and n, i.e., the number of terms being three
Arithmetic mean given as (a+b+c)/3
- Geometric Mean: – It is calculated as the product of terms with the power of inverse of the number of terms.
- For a, b, c being terms and n i.e., number of terms being three
Geometric mean is given as ∛(a x b x c)
- Harmonic Mean: – It is calculated as the number of terms divided by the summation of inverse the of each term.
- For a, b, c being terms and n i.e., number of terms being three
Harmonic mean defined as 3/(1/a+1/b+1/c)
How To Calculate Median?
The following steps will guide you to find the median of the number series.
Step 1: Arrange the numbers in descending to ascending order.
Step 2: Count the number of units in a series.
Step 3: Check if the number in Step 2 is Even or Odd
Step 4: If the Step -3 is Even, take the two digits in the center and find the average and if it is Odd, then take the middle number as the Median
For example, the series of numbers is 91, 94, 93, 89, 95, 88, 97, 87, and 100.
Step-1: 87,88, 89, 91, 93, 94,95,97, 100
Step -2: Total units in the series is 9
Step-3: Odd
Step-4: Center of the series is 5th number, median  is 93
In Microsoft Excel, you can also use the formula =MEDIAN(N1, N2, N3……)
Frequently Asked Questions
Q1. What is the difference between mean and median?
The mean is calculated by adding all values in a dataset and dividing by the number of values, while the median is the middle value when the data is arranged in ascending or descending order. Both are measures of central tendency, but they can produce different results depending on the distribution of the data.
Q2. When should the mean be used instead of the median?
The mean is most useful when the dataset is relatively symmetrical and does not contain significant outliers. It takes every value into account, making it a good representation of the overall average when extreme values are not present.
Q3. When is the median a better measure than the mean?
The median is often preferred when a dataset contains outliers or is highly skewed. Because it focuses on the middle value rather than all values, it is less affected by unusually high or low observations and may provide a more representative measure of the typical value.
Q4. How do outliers affect the mean and median?
Outliers can significantly influence the mean by pulling the average higher or lower. The median is generally less affected because it depends only on the position of values within the dataset rather than their magnitude, making it more stable in the presence of extreme observations.
Q5. Why are mean and median important in data analysis?
Mean and median help summarize large datasets and provide insights into data distribution. They are widely used in business, finance, economics, and statistics to support decision-making, identify trends, compare datasets, and better understand the characteristics of a population or sample.
