A statistical table has a subject, geographical coverage, reference period, unit and source. Read these before using any number. A value of 25 may mean persons, lakh persons, percentages or rupees in crore. Arithmetic can be correct while the interpretation is wrong because the unit or denominator was misunderstood.

All datasets in this chapter are hypothetical teaching examples. They are not Bihar government statistics and must not be quoted as current district performance. Imagine three unnamed Bihar blocks used to teach administrative analysis; the imagined setting provides context, not an official measurement.

Before comparing tables, check whether their populations and periods match. Financial year 2025–26 is not identical to calendar year 2025. A cumulative total since a scheme began is not an annual flow. Revised data should not silently be mixed with an earlier estimate for another period.

Suppose block A has 100 eligible households and 80 completed installations; block B has 200 eligible and 120 completed; block C has 300 eligible and 150 completed. The rates are 80/100 = 80%, 120/200 = 60% and 150/300 = 50%. Block C has the largest number completed but the lowest completion rate. A count and a rate answer different questions.

Overall eligible households = 100 + 200 + 300 = 600. Completed installations = 80 + 120 + 150 = 350. The combined completion rate is 350/600 × 100 = 58.33% approximately. The unweighted average of 80%, 60% and 50% is 63.33%, which is incorrect for the overall household rate because blocks have different eligible populations.

The weighted mean uses eligible households as weights: (100×80 + 200×60 + 300×50)/600 = 58.33%. An unweighted mean would answer the different question of the average of the three block rates when each block receives equal weight. Always match the weighting method to the question.

Suppose a service coverage rate rises from 40% to 50%. The increase is 10 percentage points. Its percentage increase relative to the original rate is (50−40)/40 × 100 = 25%. Calling this a 10% increase confuses two different measures of change.

If a hypothetical output index rises from 100 to 120 and then falls by 20%, it ends at 96, because 120×0.8 = 96. Equal percentage increases and decreases do not cancel when their bases differ. In general, successive percentage changes are applied multiplicatively, using factors such as 1.20 and 0.80.

A zero base requires special care. If reported cases rise from zero to ten, the ordinary percentage-growth formula divides by zero and is undefined. State the absolute change instead. Do not describe the increase as 100%, and do not invent an infinite growth rate as if it were a normal comparable statistic.

Consider hypothetical daily earnings of ₹200, ₹220, ₹230, ₹250 and ₹1,100. The total is ₹2,000, so the arithmetic mean is ₹400. The median, the middle value after ordering, is ₹230. The high observation pulls the mean above what most of the group receives. Neither statistic is inherently fraudulent; they summarise different features.

For an even number of observations, the median is the average of the two central ordered values. The mode is the most frequently occurring value and may be absent or non-unique in a small dataset. Choose the summary that fits the question and discuss distribution rather than assuming one average fully describes inequality.

If groups are combined, use their sizes when calculating a mean. A class of ten students averaging 80 and a class of thirty averaging 60 have a combined average of (10×80 + 30×60)/40 = 65, not 70. The example has the same structure as the block completion calculation.

A larger number of cases does not necessarily mean a higher risk. Suppose area X records 100 cases among 10,000 people and area Y records 60 among 3,000. The rates are 1% and 2%; Y has fewer cases but the higher rate. Use comparable definitions, periods and population-at-risk measures before ranking areas.

Missing data are not automatically zeros. If a block fails to report, entering zero completed installations understates the numerator, while dropping its eligible population without explanation can overstate coverage. Report the missingness and show how the conclusion depends on it. An honest limitation is part of the answer, not an admission that analysis has failed.

A reported rise after a new registration drive may reflect better identification rather than a sudden deterioration. Similarly, a fall may reflect under-reporting. Data production is part of interpretation: ask how the numbers were collected, which units were covered and whether the reporting process changed.

A sound conclusion from the block example is that overall recorded installation coverage is about 58.33%, with variation across the three blocks. It is not evidence that water supply is safe, continuous or equally accessible, because the table measures installations only. Match the conclusion to the variable actually observed.

Correlation is not proof of causation. If training participation and earnings are higher in the same blocks, education, prior income or employer demand may affect both. A causal claim requires an appropriate design and consideration of alternative explanations. A descriptive table can identify a pattern and motivate investigation without proving the cause.

In an exam answer, show the formula, substitute values, state the unit, interpret the result and identify a relevant limitation. This sequence earns clarity without unnecessary computation. Round only at the end where possible and label approximate results so small rounding differences are not mistaken for substantive disagreement.