Tabulation of Data — Data Analysis & Interpretation Notes for RITES Senior Technical Assistant Civil

Part 1 of 2

Data Interpretation

Last reviewed 22 Sept 2026 · 5 min read

What a DI set really tests

Not arithmetic — reading. Nearly every mark lost in this section comes from one of four things: the unit in the heading (lakh, crore, thousand), the row or column read one line off, "percentage increase" mistaken for "percentage point", or an average taken over the wrong number of years.

Read in this order: title → unit → row and column headings → the question. Only then look at the numbers.

The four presentations

Type	What it is good at	Watch out for
Table	exact values, several variables	which way the years run
Bar chart	comparing quantities	the scale, and bars that do not start at zero
Line graph	trend over time	a broken axis exaggerating a rise
Pie chart	shares of one whole	two pies with different totals

A caselet presents the same data as a paragraph of prose; convert it into a small table before answering anything.

The five questions

FormulaThe recurring calculations

Total of a row or column — plain addition
Average $= \frac{total}{number of entries}$ (count the entries, do not assume five)
Ratio — reduce before dividing
Percentage share $= \frac{part}{whole} \times 100$
Percentage change $= \frac{new - old}{old} \times 100$ — always over the old value

For pie charts: $1% = 3.6°$ , so a sector of $54°$ is $15%$ . Two pie charts can only be compared in absolute terms if both totals are given.

Working quickly

Keep the unit out of the arithmetic: if everything is "₹ lakh", work in plain numbers and put the unit back at the end.
Use fraction equivalents rather than long division: $\frac{1}{8} = 12.5%$ , $\frac{1}{7} \approx 14.3%$ , $\frac{1}{6} \approx 16.7%$ , $\frac{1}{3} \approx 33.3%$ .
When options are far apart, approximate: $\frac{85}{180}$ is a little under half, so 47% is right and 43% is not.
Do not recompute a total you already worked out for the previous question — DI sets are built so each answer feeds the next.

A worked set

The table shows the sales of two products, in ₹ lakh.

Year	Product A	Product B	Total
2021	40	60	100
2022	55	65	120
2023	70	80	150
2024	60	90	150
2025	85	95	180

Worked ExampleQuestion 1 — total

What are the total sales of product A over the five years?

Solution. $40 + 55 + 70 + 60 + 85 =$ ₹ 310 lakh.

Worked ExampleQuestion 2 — average

Find the average annual sales of product B.

Solution. $\frac{60 + 65 + 80 + 90 + 95}{5} = \frac{390}{5} =$ ₹ 78 lakh.

Worked ExampleQuestion 3 — percentage change

By what percent did the total sales grow from 2021 to 2025?

Solution. $\frac{180 - 100}{100} \times 100 =$ 80%.

Worked ExampleQuestion 4 — percentage share

In which year was product A's share of the total the highest?

Solution. Shares: $40%$ , $45.8%$ , $46.7%$ , $40%$ , $47.2%$ → 2025.

Worked ExampleQuestion 5 — ratio

Find the ratio of the sales of A to B in 2023.

Solution. $70 : 80 =$ 7 : 8.

Worked ExampleQuestion 6 — year-on-year growth

Find the percentage increase in the sales of A from 2022 to 2023.

Solution. $\frac{70 - 55}{55} \times 100 = \frac{15}{55} \times 100 \approx$ 27.3%.

Worked ExampleQuestion 7 — a trap

Product A's share rose from 40% in 2024 to 47.2% in 2025. Is that a rise of 7.2% or of 7.2 percentage points?

Solution. 7.2 percentage points. As a percentage increase it is $\frac{7.2}{40} \times 100 = 18%$ . The two are different numbers and the options will contain both.

Worked ExampleQuestion 8 — as a pie chart

If the 2025 sales are drawn as a pie chart, what angle does product A occupy?

Solution. $\frac{85}{180} \times 360° =$ 170°.

Worked ExampleQuestion 9 — a year below the average

In how many years were product A's sales below their own five-year average?

Solution. Average $= 310/5 = 62$ → 2021 (40), 2022 (55) and 2024 (60) are below it: 3 years.

Worked ExampleQuestion 10 — combining rows

If the company earns a profit of 20% on A and 15% on B, what is the profit in 2024?

Solution. $0.20 \times 60 + 0.15 \times 90 = 12 + 13.5 =$ ₹ 25.5 lakh.

Frequently tested points

Read the unit in the heading before any calculation.
Percentage change is over the old value; a share in percent changes by percentage points.
Average needs the count of entries actually being averaged.
Pie chart: $1% = 3.6°$ ; comparing two pies needs both totals.
A bar chart whose axis does not start at zero exaggerates differences.
Reduce ratios before dividing, and reuse totals already computed.
Approximate when the options are far apart; compute exactly only when they are close.

Common MistakeCommon mistakes

Dividing by the new value in a percentage change.
Treating a rise from 40% to 47.2% as a 7.2% increase.
Averaging over five years when the question asks about four.
Comparing sectors of two pie charts as though the totals were equal.
Losing the unit — answering 310 when the answer is ₹ 310 lakh.

Revision SummaryChapter summary

Data interpretation rewards careful reading of the title, unit and headings before the numbers.
Tables, bar charts, line graphs, pie charts and caselets present the same kinds of data with different traps.
Five calculations — total, average, ratio, share and percentage change — cover almost every question asked.
Percentage change and percentage points are different, and both appear in the options.
Speed comes from fraction equivalents, approximation and reusing totals, not from faster long division.

Part 2 of 2

Elementary Statistics

Last reviewed 22 Sept 2026 · 6 min read

Frequency distributions

Raw data is grouped into classes with frequencies. For a class such as 20–30: the class mark (midpoint) is 25, the class size is 10, and the cumulative frequency is the running total of the frequencies up to that class. In an exclusive distribution (10–20, 20–30) the upper limit belongs to the next class; in an inclusive one (10–19, 20–29) it does not, and the limits must be corrected by half the gap before any formula is used.

The three averages

FormulaMean

Ungrouped: $\overset{x}{ˉ} = \frac{\sum x}{n}$
Grouped: $\overset{x}{ˉ} = \frac{\sum f x}{\sum f}$ with $x$ the class mark
Assumed mean: $\overset{x}{ˉ} = A + \frac{\sum f d}{\sum f}$ , where $d = x - A$
Step deviation: $\overset{x}{ˉ} = A + h \frac{\sum f u}{\sum f}$ , where $u = \frac{x - A}{h}$
Combined mean of two groups: $\frac{n _{1} x ˉ _{1} + n _{2} x ˉ _{2}}{n _{1} + n _{2}}$

FormulaMedian and mode

Ungrouped (data arranged in order):

$n$ odd → the $(\frac{n + 1}{2})$ th value; $n$ even → the mean of the two middle values.
Mode is the most frequent value; a set may have none or several.

Grouped:

Median = l + \frac{\frac{N}{2} - c f}{f} \times h, Mode = l + \frac{f _{1} - f _{0}}{2 f _{1} - f _{0} - f _{2}} \times h

where $l$ is the lower limit of the median or modal class, $N = \sum f$ , $c f$ the cumulative frequency before it, $f$ its frequency, $h$ the class size, and $f_{0}, f_{1}, f_{2}$ the frequencies of the classes before, at and after the modal class.

Empirical relation: $Mode = 3 Median - 2 Mean$ .

Which one to use: the mean uses every value but is dragged by extremes; the median ignores extremes and suits skewed data such as incomes; the mode is the only average for a non-numeric category.

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Data Interpretation

What a DI set really tests

The four presentations

The five questions

Working quickly

A worked set

Frequently tested points

Elementary Statistics

Frequency distributions

The three averages

Finished reading? Test yourself.