Chapter 7: Data Handling, Patterns & Symmetry
आंकड़ों का प्रबंधन, माध्य, माध्यक, बहुलक एवं सममिति
Don't Let a 20-Minute Bubbling Delay Cost You CTET Qualification
In offline CTET exams, bubbling 150 bubbles takes 18 to 22 minutes of mechanical time. A single misaligned row can trigger an 8-question domino error. Practice bubble-filling this chapter's solved MCQs inside Mentora's official OMR simulator.
- Measures of Central Tendency: Mean (Arithmetic average: sum of observations / total number); Median (Middle value when data is arranged in ascending order; if n is even, average of middle two values); Mode (Most frequently occurring observation).
- Impact of Outliers: Extreme outlier values distort the MEAN significantly, whereas the MEDIAN remains robust and representative of skewed data.
- Line Symmetry (Reflectional Symmetry): An imaginary fold line dividing a figure into two identical mirror halves. A circle has infinite lines of symmetry; a square has 4; a rectangle has 2; an equilateral triangle has 3; a scalene triangle has 0.
- Rotational Symmetry: The number of times a figure coincides with its original outline during a 360° rotation. Order of rotational symmetry: Square = 4 (every 90°); Rectangle = 2 (every 180°); Equilateral triangle = 3 (every 120°).
- Trap: How many lines of symmetry does a rectangle have? Correct: **2 lines of symmetry** (horizontal and vertical). Diagonal lines are NOT lines of symmetry for a rectangle.
- Trap: Which measure of central tendency is best when extreme outliers are present? **The Median (माध्यक)**.
NCERT Core Facts: Statistical Measures & Geometric Symmetry
In CTET Paper 1 and Paper 2, statistics and symmetry questions evaluate analytical precision:
1. Comparing Mean, Median, and Mode
- Mean (माध्य): bar{x} = (∑ x_i)/(n). Sensitive to extreme values.
- Median (माध्यक): Value separating higher half from lower half.
- Arrange in ascending order.
- If n is odd: Median = left((n+1)/(2)right)^th item.
- If n is even: Average of left((n)/(2)right)^th and left((n)/(2) + 1right)^th items.
- Mode (बहुलक): The observation with highest frequency.
- Empirical Relationship: Mode = 3 Median - 2 Mean.
2. Symmetry of Common Polygons and Alphabets
| Shape / Letter | Lines of Symmetry | Order of Rotational Symmetry |
|---|---|---|
| Square | 4 | 4 (90^circ) |
| Rectangle | 2 | 2 (180^circ) |
| Equilateral Triangle | 3 | 3 (120^circ) |
| Circle | Infinite | Infinite |
| Letter 'H' / 'X' | 2 | 2 |
| Letter 'O' | Infinite (circle) | Infinite |
| Letter 'Z' | 0 | 2 (180^circ) |
Test Your Mastery: Data Handling, Patterns & Symmetry
Authentic CBSE exam questions tested directly from this NCERT chapter.
Find the median of the following dataset: 7, 12, 5, 9, 14, 18, 10, 8, 15.
निम्नलिखित आंकड़ों का माध्यक (Median) ज्ञात कीजिए: 7, 12, 5, 9, 14, 18, 10, 8, 15।
Which of the following English capital letters has BOTH reflectional line symmetry and rotational symmetry of order 2?
निम्नलिखित में से किस अंग्रेजी वर्णमाला के बड़े अक्षर में रैखिक सममिति और घूर्णन सममिति (क्रम 2) दोनों होती हैं?
How many lines of symmetry does a standard non-square rectangle possess?
Exactly 2 lines of symmetry (horizontal and vertical bisectors of opposite sides).
Which central tendency measure is least affected by extreme outlier scores?
The Median.