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Mean, median, and mode are the three main measures of central tendency. They help you understand the “center” or most typical value in a set of numbers. While they all give insight into your data, each one works slightly differently and is useful in different situations.
🔹 Mean (Average)
What it is: The sum of all values divided by the number of values.
Formula: Mean = (Sum of all values) ÷ (Number of values)
When to use: When you want the overall average, and your data doesn’t have extreme outliers.
📊 Example:
Data: 5, 10, 15
Mean = (5 + 10 + 15) ÷ 3 = 30 ÷ 3 = 10
✅ Interpretation: The average value in the dataset is 10.
🔹 Median (Middle Value)
What it is: The middle value when all numbers are arranged in order.
When to use: When your data has outliers or is skewed, and you want the true center.
📊 Example:
Data: 3, 7, 9, 12, 50
Sorted order → Middle value = 9
(Median is not affected by 50 being much larger.)
✅ Interpretation: Half the values are below 9 and half are above.
🔹 Mode (Most Frequent Value)
What it is: The number that appears most often in the dataset.
When to use: When you want to know which value occurs the most (especially for categorical data).
📊 Example:
Data: 2, 4, 4, 4, 6, 7
Mode = 4 (because it appears the most)
✅ Interpretation: The most common value in the dataset is 4.
📌 Summary Table:
Measure | Best For | Sensitive to Outliers? | Works With |
---|---|---|---|
Mean | Average of all values | Yes | Numerical data |
Median | Center value | No | Ordered numerical data |
Mode | Most frequent value | No | Numerical or categorical data |
Length of the train = 132 meters
Time taken to pass a telegraph pole = 6 seconds
—
✅ Step 1: Use the formula for speed:
Speed = Distance ÷ Time
= 132 m ÷ 6 s = 22 meters/second
—
✅ Step 2: Convert m/s to km/h:
1 m/s = 3.6 km/h
⇒ 22 × 3.6 = 79.2 km/h
—
✅ Final Answer: The speed of the train is 79.2 km/h.