Mean, median, mode, and standard deviation are basic but powerful tools in statistics. They help us understand what’s typical in a set of numbers and how much things vary. Whether it's exam marks, daily temperatures, or survey results, these tools make sense of the data!
1. Mean (Average)
The mean is what we usually call the "average." Just add all the numbers and divide by how many there are.
Mean = (Total of all values) ÷ (Number of values)
- Easy to calculate and understand.
- Can be unfair if there are extreme numbers (like one super high score).
2. Median
The median is the middle number when all numbers are lined up from smallest to biggest. If there are two middle numbers, take their average.
- Great for when data has a few really big or small numbers.
- Shows the “center” without being affected by outliers.
3. Mode
The mode is the number that shows up the most in a list. Some lists can have two or more modes—or none!
- Useful for finding what’s popular or common (like favorite snacks).
- Works well with names, colors, and other categories too.
4. Standard Deviation
This sounds complex, but it just tells you how spread out your data is. Are most values close to the average, or are they all over the place?
SD = √(∑(x - mean)² ÷ n) (for full data)
SD = √(∑(x - mean)² ÷ (n - 1)) (for sample)
- Small SD = values are tightly packed.
- Large SD = values are widely spread out.
5. Grouped vs. Ungrouped Data
Ungrouped Data: Raw numbers like 45, 56, 70, 65...
Grouped Data: Data organized into intervals like "40–50", "51–60", etc.
- Grouped data uses midpoints to calculate mean and other stats.
- The ideas stay the same—just the steps change slightly.
6. Summary
- Mean: Good overall summary, but watch for outliers.
- Median: Best when data is skewed or uneven.
- Mode: Great for finding what's most common.
- Standard Deviation: Shows how much things vary from the average.