When we discuss measures of central tendency in statistics, we focus on three important ideas: mean, median, and mode. Each one helps us look at data in different ways, making it easier to understand.

1. Mean: The Average

The mean is what many people call the average. To find the mean, you add up all the numbers in a data set and then divide by how many numbers there are.

Example: Let’s say you have these test scores: 70, 85, 90, 95, and 100.

To find the mean:

• First, add the scores: $70 + 85 + 90 + 95 + 100 = 440$.
• Then divide by the number of scores: $\frac{440}{5} = 88$.

So, the mean score is $88$. This number helps us understand how well the students did overall. But, if one student scored really low, like $30$, the mean would drop to $81$ ($\frac{410}{5}$). This shows how outliers can change the average.

2. Median: The Middle Value

The median is the middle number when you put the numbers in order from smallest to largest. It splits the data into two equal parts and is helpful when the data has some really high or low numbers.

Example: If we add a new score of $60$ to our previous scores, we now have: 60, 70, 85, 90, 95, 100.

To find the median:

• First, list the scores in order: 60, 70, 85, 90, 95, 100.
• Since there are six scores (an even number), the median is the average of the two middle scores: $\frac{85 + 90}{2} = 87.5$.

Here, the median is $87.5$. This number is more reliable than the mean because it isn’t affected as much by that low score of $60$.

3. Mode: The Most Frequent Value

The mode is the score that appears most often in a data set. A set can have one mode (unimodal), two modes (bimodal), or more (multimodal). The mode is especially useful when you want to know which category is the most common.

Example: Imagine students picked their favorite colors, and the results were: Red, Blue, Blue, Green, Red, Red.

Here’s how often each color was picked:

• Red: 3 times
• Blue: 2 times
• Green: 1 time

So, the mode is Red, since it was chosen the most.

Summary: Different Perspectives

• Mean gives us the average performance, but it can change if there are extreme scores.
• Median shows us the middle value and is better for data that’s not balanced.
• Mode points out which item or choice is the most popular, helping us see trends.

By learning how to find and understand mean, median, and mode, we can choose the best way to look at our data and share important information. Each measure helps us see different parts of the story behind the numbers!