Statistics (NCERT Ch. 12)

• Collect ungrouped and grouped data.
• Compute mean of ungrouped data and by direct, assumed mean, step-deviation methods for grouped data.
• Find median of grouped data using cumulative frequency.
• Draw and interpret histograms and frequency polygons.

1. Data — Raw facts; frequency — how often a value occurs.
2. Mean (ungrouped) — Sum of observations ÷ number.
3. Grouped mean — Σfixi / Σfi using class marks.
4. Assumed mean method — Reduce calculation using deviation di = xi − a.
5. Median (grouped) — L + [(N/2 − cf)/f] × h formula.
6. Histogram — Area ∝ frequency; equal class widths → height ∝ frequency.
7. Frequency polygon — Line graph of midpoints vs frequencies.
8. NCERT — interpret real-life tables (marks, wages).

Find mean of 5, 7, 8, 10, 10.

Sum = 40, n = 5 → mean = 8.

• Skipping given-to-prove structure in geometry proofs.
• Using wrong congruence criterion (SSA is not valid).
• Forgetting units in length/angle statements.

• State one NCERT result from Statistics.
• Draw a neat diagram for a typical Statistics problem.

Open the Practice tab for graded questions on Statistics (NCERT Ch. 12).