🧠 Key Definitions with Examples
Data: A collection of facts or numbers used for a purpose.
Example: Marks of 5 students: 45, 48, 50, 40, 42
Types of Data:
- Primary Data: Collected by yourself. E.g., asking friends their favorite food.
- Secondary Data: Taken from books/websites. E.g., data from newspapers.
Observation: Each number in data is an observation.
Example: In [12, 15, 18], 12 is an observation.
Range: Difference between highest and lowest values.
Range = Highest - Lowest
Example: In [12, 22, 18], Range = 22 - 12 = 10
Average (Mean): Central value of data.
Mean = Sum of observations / Number of observations
Example: [50, 60, 70] → Mean = 180 / 3 = 60
Median: The middle value in a sorted list of data. It divides the data into two equal parts.
Steps to Find Median:
- Arrange the data in ascending (or descending) order.
- Count the number of values, let it be
N.
-
If
N is odd: Median is the value at position (N + 1) / 2.
If N is even: Median is the average of values at positions N / 2 and (N / 2) + 1.
Odd Example: [5, 10, 15] → Median = 10 (middle value)
Even Example: [2, 4, 6, 8] → Median = (4 + 6)/2 = 5
More Example:
Data: [12, 16, 11, 14, 13] → Order = [11, 12, 13, 14, 16] → Median = 13
Data: [3, 5, 7, 9, 11, 13] → Median = (7 + 9)/2 = 8
Mode: The value or values that appear most frequently in a data set.
Note: If two or more values repeat the same highest number of times, the data has multiple modes (called bimodal, trimodal, etc.).
Examples:
1. [2, 3, 3, 4, 5, 3] → Mode = 3 (appears most often)
2. [4, 4, 5, 5, 6, 6] → Modes = 4, 5, and 6 (all appear twice)
3. [7, 8, 9, 10] → No mode (all appear once)
Bar Graph: Picture using bars to show data.
Example: Students in Class A = 30, Class B = 40
Double Bar Graph: Two bars side-by-side for comparing two data sets.
Example: Comparing marks of two students in 5 subjects