Class 10 Maths Chapter 13 Statistics Revision Notes

Reference figure: a histogram of grouped data, illustrating how frequency-distribution data used throughout this chapter is visualised.

Last Updated: September 23, 2026

Common Mistakes Students Make in Statistics

Class 10 Maths Chapter 13 – Statistics: Quick Revision Notes

• Class mark xᵢ = (Upper limit + Lower limit)/2
• Mean (Direct): x̄ = Σfᵢxᵢ/Σfᵢ
• Mean (Assumed Mean): x̄ = a + Σfᵢdᵢ/Σfᵢ, dᵢ=xᵢ-a — use for unequal class widths
• Mean (Step-Deviation): x̄ = a + (Σfᵢuᵢ/Σfᵢ)×h, uᵢ=(xᵢ-a)/h — use for equal widths, large numbers
• All three mean methods always give the same numeric answer
• Inclusive/gapped classes must be converted to continuous classes first (adjust limits by half the gap)
• Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)] × h — modal class = class with highest frequency
• Median = l + [(n/2-cf)/f] × h — median class = first class whose cf ≥ n/2, found from a cumulative frequency table
• “Less than” cumulative tables must be converted to individual class frequencies before use
• Empirical relationship: Mode = 3 Median − 2 Mean (equivalently 3 Median = Mode + 2 Mean)
• Ogive: less-than ogive rises (upper limits vs cf); more-than ogive falls (lower limits vs cf); their intersection’s x-coordinate gives the median graphically
• Common trap: modal class = highest frequency, NOT highest cumulative frequency

More on This Chapter

• NCERT Solutions – Chapter 13
• Extra Questions (HOTS) – Chapter 13
• Revision Notes – Chapter 13
• Class 10 Maths Book (Catalog Page)

Frequently Asked Questions

Which method is fastest for calculating the mean of grouped data: direct, assumed-mean, or step-deviation?
The step-deviation method is usually fastest when class sizes are equal and class marks are large, since it reduces big numbers to small, easy-to-handle values before scaling back — but all three methods give the same final answer, so choose based on which is quickest for the specific numbers given.

How is the median of grouped data found using an ogive (cumulative frequency curve)?
Plot the cumulative frequency against the upper class limits to draw the ogive, then locate n/2 on the cumulative frequency axis and read across to find the corresponding class — this graphical method is an alternative to the formula-based approach and is sometimes asked directly in exams.

What to Revise First (and Last) in This Chapter

Written by Satish

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