Mean (direct, assumed-mean and step-deviation methods), mode and median of grouped data. Our own step-by-step solutions to Exercises 13.1 to 13.3, one page per exercise, set out for step marks.
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What it tests. Use class mid-points \(x_i\). Direct method: \(\bar x = \dfrac{\sum f_ix_i}{\sum f_i}\). With large numbers use an assumed mean \(a\): \(\bar x = a + \dfrac{\sum f_id_i}{\sum f_i}\), or step deviations \(u_i = \dfrac{x_i - a}{h}\): \(\bar x = a + h\dfrac{\sum f_iu_i}{\sum f_i}\). All give the same answer.
What it tests. The modal class has the highest frequency. Mode \(= l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h\), where \(f_0, f_2\) are the frequencies of the classes before and after it. Mode is best for 'most common', mean for 'average'.
What it tests. Build the cumulative frequency column, find \(\tfrac n2\), take the first class whose cumulative frequency reaches it, then Median \(= l + \dfrac{\frac n2 - cf}{f} \times h\) (cf is the cumulative frequency before that class). For inclusive classes like 118–126, first convert to boundaries 117.5–126.5.
Statistics has 37 original board-style questions (MCQ, assertion–reason, short and long answers, case studies) with step mark schemes, revision notes and a four-step Route to 95. Three sample questions are open to everyone; a free account opens the rest.
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Textbook: NCERT Mathematics Class 10 (rationalised edition, 2023-24 reprint onward), free from ncert.nic.in. Question statements are shortened to the minimum needed; the solutions and tips are our own. CBSE Math Revision is independent and not affiliated with NCERT or CBSE. Spotted a slip? Tell us and it goes in the corrections log.