Class 10 Maths Chapter 13: Statistics Concept Infographic (NCERT)

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✦ NCF 2023 ALIGNED • VISUAL LEARNING SERIES ✦

Chapter 13: Statistics

Mastering Grouped Data: Mean, Mode, Median, and Empirical Relations[cite: 13].

📊 1. Mean (x̄)

Three methods for grouped data mean[cite: 13]:

Direct Method:

x̄ =

∑f_ix_i∑f_i

[cite: 13]

Assumed Mean Method:

x̄ = a +

∑f_id_i∑f_i

[cite: 13]

Step-Deviation Method:

x̄ = a + (

∑f_iu_i∑f_i

)h

[cite: 13]

📈 2. Mode

Most frequent value (Modal Class)[cite: 13].

Mode Formula

Mode = l +

f₁ - f₀2f₁ - f₀ - f₂

× h[cite: 13]

Where: l = lower limit[cite: 13], h = size[cite: 13], f₁ = modal freq.[cite: 13], f₀, f₂ = preceding & succeeding freq.[cite: 13].

📉 3. Median

Middle observation using Cumulative Frequency (cf)[cite: 13].

Median Formula

Median = l +

n/2 - cff

× h[cite: 13]

Where: l = lower limit[cite: 13], n = total freq.[cite: 13], cf = preceding cf[cite: 13], f = median freq.[cite: 13].

⭐ Board Exam Super-Hacks

The Empirical Relationship

If any two measures (Mean, Median, or Mode) are given, you can find the third instantly using this golden formula[cite: 13]:
3 Median = Mode + 2 Mean[cite: 13]

Step-Deviation Shortcut

Always choose ‘a’ as the class mark right in the middle of the table, and 'h' as the common class size to keep your u_i values small (-2, -1, 0, 1, 2)[cite: 13]!

⚠️ Common Exam Traps

Trap 1: Discontinuous Class Intervals

If intervals are given like 1-3, 4-6 (discontinuous), you MUST convert them to continuous classes (0.5-3.5, 3.5-6.5) by subtracting 0.5 from lower limits and adding 0.5 to upper limits before finding the median or mode[cite: 13]!

Trap 2: Cumulative Frequency Mistake

In the Median formula, cf is the cumulative frequency of the class preceding the median class, NOT of the median class itself[cite: 13]!

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