When it comes to statistics, two important numbers we often use are the mean and the median. These numbers help us understand what's typical or average in a group of data. But how are they different? Let's explore this in an easy and practical way, using everyday examples.
The Mean:
The mean is also known as the average. It's found by adding up all the numbers in a group and then dividing the total by how many numbers there are. The mean shows us the central value that represents the general trend of the data.
Mean = sum of numbers/ quantity of numbers
Example 1: Let's say you have a class of five students, and you want to find the mean of their test scores. The scores are 75, 80, 65, 90, and 85. To find the mean, you add up all the scores and divide by the number of students. In this case, the mean score is 79. This gives us an idea of how the students performed overall in the test.
Mean = 75 + 80 + 65 + 90 + 85/5 = 79
Example 2: Imagine you have a small company with five employees, and you want to find the mean of their salaries. The salaries are $30,000, $40,000, $50,000, $80,000, and $1,000,000.
Mean = 30000 + 40000 + 50000 + 80000 + 1000000/5 = 240000
The Median:
The median is different from the mean. It represents the middle value when all the numbers are arranged in order. If there is an even number of numbers, the median is the average of the two middle values. The median is less sensitive to extreme values and gives us an idea of what's typical in the group.
For even numbers
Median = pick two middle values after arranging in ascending order /2
For odd numbers
Median = middle value will be single in this case
Example 1: Let's go back to the student scores from Example 1. If we arrange the scores in order from lowest to highest, we have 65, 75, 80, 85, and 90. Since there is an odd number of scores, the median is the middle value, which is 80. This tells us what a typical score would be.
Median(5 is an odd number) = so middle value is 80
Example 2: Using the salary data from Example 2, if we arrange the salaries in order, we have $30,000, $40,000, $50,000, $80,000, and $1,000,000.
Median(5 salaries are given;odd number) =so median would be $50000.
To sum it up, the mean and median are both important in statistics, but they tell us different things about a group of data. The mean gives us an overall view and can be affected by extreme values, while the median shows us the middle value and is less affected by outliers. Choosing which one to use depends on the data and the specific question we want to answer.
In conclusion, understanding the difference between mean and median is helpful when analyzing data. By knowing how they work and when to use each one, we can gain valuable insights from our data and make better decisions.