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Chapter 13 · Question 3

When is the step-deviation method useful? State its formula.

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Q3

When is the step-deviation method useful? State its formula.

Answer Revealed
Direct Answer:
It is useful when class marks have a common factor in their deviations. Let ui=xi−ahu_i=\frac{x_i-a}{h}. Then xˉ=a+h∑fiui∑fi\bar{x}=a+h\frac{\sum f_i u_i}{\sum f_i}.

Simple Explanation

Divide deviations by class width to make numbers smaller.

Exam-Ready Structure

If all di=xi−ad_i=x_i-a are multiples of a common number hh, define ui=dihu_i=\frac{d_i}{h}. Then the mean is xˉ=a+h∑fiui∑fi\bar{x}=a+h\frac{\sum f_i u_i}{\sum f_i}. This simplifies arithmetic for large grouped data.

Key Points

  • It is useful when class marks have a common factor in their deviations.
  • Use the NCERT formula or theorem carefully.
  • Write units and final conclusion where applicable.

Related Questions

Q4

State the formula for mode of grouped data and define the terms.

Q5

State the formula for median of grouped data.

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