NDA Statistics: Data, Central Tendency, Dispersion, Correlation and Regression

Owned by UPSC NDA Mathematics syllabus. Exact NDA-relevant scope: Classification of data; frequency and cumulative frequency distributions; histogram, pie chart and frequency polygon; mean, median and mode; variance and standard deviation; correlation and regression.

Classification of data; frequency and cumulative frequency distributions; histogram, pie chart and frequency polygon; mean, median and mode; variance and standard deviation; correlation and regression.

Arithmetic, percentages, ratios, algebraic substitution and graph reading.

• Frequency distribution
• Cumulative frequency
• Mean, median and mode
• Variance and standard deviation
• Correlation
• Regression

• Ungrouped mean: xbar = sum x / n
• Frequency mean: xbar = sum f x / sum f
• Population-style variance for a finite dataset: sigma^2 = sum (x-xbar)^2 / n, with denominator chosen to match the problem definition
• Standard deviation sigma=sqrt(variance)
• Pie-chart sector angle = category frequency / total x 360 degrees
• For grouped median / mode, use the formula only when class structure and frequencies fit the standard grouped-data assumptions taught for the problem.

• Always identify whether data are raw, discrete-frequency or grouped-continuous before choosing a formula.
• Grouped formulas depend on class intervals and the intended frequency treatment.
• Correlation measures association, not causation.
• Regression line use requires consistent variable roles and scale.
• Do not mix sample and population variance conventions without reading the question.

1. Data 2,4,4,6: mean=4; squared deviations 4,0,0,4 sum to 8; using denominator n gives variance 2 and SD sqrt2.
2. A category with 30 observations out of 120 gets 30/120 x 360=90 degrees in a pie chart.
3. If cumulative frequencies are 5, 12, 20, 31, the median class is located by the position near N/2, not by choosing the largest class frequency.

• Using ordinary mean when frequencies are supplied.
• Confusing cumulative frequency with class frequency.
• Applying grouped-mode formula blindly to unsuitable or unequal-width classes.
• Treating high correlation as proof that one variable causes the other.
• Forgetting that SD is the square root of variance.

• Knowledge Gap: The concept, definition or theorem needed to solve the item is not understood.
• Recall Gap: The concept was learned but a formula, condition or relation cannot be retrieved accurately.
• Execution Error: The correct method is known but algebra, arithmetic, sign, substitution, diagram or step execution fails.
• Decision / Selection Error: The candidate chooses an inefficient method, continues a time-heavy path, or attempts a low-confidence item without adequate basis.
• Needs Review: Evidence is insufficient or contradictory; do not mislabel the error until another worked item is checked.
• Time pressure note: Time pressure is treated as a contributing condition, not automatically as the root cause.

Identify the representation first: table, graph or raw list. For central tendency, choose the measure requested and avoid unnecessary conversion. For grouped data, write class boundaries / frequencies before formula use. For correlation / regression, interpret sign and relation cautiously and compute only what the question asks.

Negative marking is a real exam condition, but this page does not promise a universal attempt threshold. Use method certainty and option evidence before committing to a low-confidence answer.

• Required reviewer: NDA Mathematics faculty with demonstrable subject competence.