Statistics — Notes

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Chapter 13: Statistics

Grouped Data, Mean, Assumed Mean, Step-Deviation and Cumulative Frequency

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01 13.1 Grouped Data

For grouped observations, class intervals are accompanied by frequencies. The class mark is the midpoint of a class interval: x_i=(upper limit+lower limit)/2.

02 13.2 Mean by Direct Method

For grouped data, Mean = Σf_ix_i / Σf_i.

03 13.3 Assumed Mean Method

Choose an assumed mean A and let d_i=x_i−A. Then:
Mean = A + Σf_id_i/Σf_i.

04 13.4 Step-Deviation Method

When class marks have a common class width h, let u_i=(x_i−A)/h. Then:
Mean = A + h(Σf_iu_i/Σf_i).

05 13.5 Median of Grouped Data

For grouped data, identify the median class using N/2 in the cumulative-frequency column, then apply the grouped-data median formula:
Median = l + [(N/2 − cf)/f]h.

06 13.6 Mode of Grouped Data

Identify the modal class with the highest frequency and use:
Mode = l + [(f₁−f₀)/(2f₁−f₀−f₂)]h.

⚡ Quick Revision

🎯 Board Exam Focus

✔ Read every formula with its conditions and symbols.

✔ Write given data first and keep units consistent.

✔ For proofs, state the theorem and show logical steps.

✔ Check signs, substitutions and final units.