Central tendency 101

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1. Mean (Arithmetic Mean - A.M.)

• Used in: Q2, Q7, Q12, Q13, Q15, Q24, Q25, Q32, Q33, Q38, Q39, Q41, Q48, Q49

• Concept: A.M = Sum of observations / Number of observations

• Arithmetic Mean

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2. Median

• Used in: Q6, Q14, Q17, Q21, Q26, Q35, Q42, Q49

• Concept: The middle value when data is ordered. For grouped data, use formula:

  Median

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• Given previously.

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3. Mode

• Used in: Q5, Q8, Q20, Q23, Q30, Q34, Q49

• Concept: The most frequent value. For grouped data:

  Mode

• 

• Given previously

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4. Relations Between Mean, Median & Mode

• Used in: Q1, Q20, Q30, Q31

• Formula:

  Mode=3×Median−2×Mean

• This formula is enough.

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5. Geometric Mean (G.M.)

• Used in: Q10, Q16, Q22, Q27, Q43, Q45

• 

• I will show you.

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6. Harmonic Mean (H.M.)

• Used in: Q9, Q18, Q22, Q44, Q51

• Concept:

  

• I will show you.

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7. Combined Mean

• Used in: Q12, Q24, Q32, Q33, Q39, Q48

• Formula:

• 

• Combined mean

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8. Correcting the Mean

• Used in: Q13, Q15, Q25, Q41, Q52

• Concept: Adjust the total and divide by the number of observations.

• Corrected Mean Calculation

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9. Missing Frequency (Given Mean or Median)

• Used in: Q4, Q21, Q34, Q35, Q42, Q46, Q50

• Technique: Use formula-based approach to form equation(s) and solve.

• Finding Missing Frequencies | Mean Given

• Finding Missing Frequencies

• another example

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10. Grouped Data (Mean, Median, Mode)

• Used in: Q3, Q14, Q26, Q40, Q49

• Class intervals and frequencies used to calculate:

• Mean, Median, Mode for Grouped Data | Full Tutorial

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11. Frequency Curve (Highest Point)

• Used in: Q11, Q36

• Concept: Mode represents the peak of the frequency curve. ( enough info)

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12. Speed-Based Averages (Harmonic Mean Context)

• Used in: Q50

• When distance is same, use:

• I will show you.

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13. Inequality of Means (A.M ≥ G.M ≥ H.M)

• Used in: Q18, Q19, Q22, Q29

• Concept: Arithmetic Mean ≥ Geometric Mean ≥ Harmonic Mean. ( Fact to remember)

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