Tables: Quantitative Aptitude Notes for Tripura Patwari / Lekhpal

Study Notes – Tables

(For Tripura Patwari / Lekhpal – Quantitative Aptitude)

Tables are a systematic way of arranging data so that it can be read, compared and analyzed quickly.
In the Patwari/ Lakhpal exam, tables often appear in the context of frequency, cumulative frequency, contingency (cross‑tabulation) and probability problems.

1. Simple Explanation

Type	What it shows	Typical use in exam
Frequency Table	How often a particular value occurs.	Counting items, calculating mean/median.
Cumulative Frequency Table	Running total of frequencies up to a given value.	Finding the position of a value, e.g., median or percentile.
Contingency (Cross‑Tabulation) Table	Joint distribution of two categorical variables.	Finding probabilities of joint events, conditional probabilities.
Relative Frequency / Probability Table	Frequency divided by total count (or probability of each event).	Probability questions, expected value calculations.

In all these tables, rows usually represent the values (or categories) and columns represent the count or frequency (or other derived measures).

2. Key Points

#	Topic	Key Points	Typical Exam Question
1	Constructing a Frequency Table	• List all distinct values in ascending order. • Write frequency of each value next to it. • Check that the sum of frequencies = total items.	“A teacher recorded the number of students who scored 50, 60, 70, 80, 90 out of 100. Build a frequency table.”
2	Cumulative Frequency	• Add frequencies from left to right. • Useful for determining the median (value where cumulative frequency ≥ half the total).	“Find the median score from the table below.”
3	Relative Frequency / Probability	• Relative frequency = ( \frac{f}{N} ). • If total probability must sum to 1, use relative frequencies directly.	“What is the probability that a randomly selected student scored 80?”
4	Contingency Table	• Two categorical variables: rows one variable, columns another. • Marginal totals = sum across rows/columns. • Joint probability = cell count / total.	“Probability that a student is male and scored > 70.”
5	Using Tables for Percentiles	• Find the class (row) where cumulative frequency ≥ desired percentile × total. • Interpolate if necessary.	“What score corresponds to the 80th percentile?”
6	General Tips	• Always double‑check totals & sums. • For quick answers, use cumulative frequencies for median/percentile. • For probabilities, convert counts to fractions early.	–

3. Worked Example

Problem
A village had 120 households. The number of rooms in each household was recorded as follows:

Rooms	Frequency
1	8
2	12
3	18
4	30
5	22
6	10
7	12
8	10

Build a cumulative frequency table.
Find the median number of rooms.
What is the probability that a randomly chosen household has at least 5 rooms?

Step 1 – Cumulative Frequency

Rooms	Frequency	Cumulative Frequency
1	8	8
2	12	20
3	18	38
4	30	68
5	22	90
6	10	100
7	12	112
8	10	122

Corrected Table

Rooms	Frequency	Cumulative Frequency
1	8	8
2	12	20
3	18	38
4	30	68
5	22	90
6	10	100
7	12	112
8	8	120

Note: total = 120.

Step 2 – Median

Median position = ( \frac{120}{2} = 60 ).
Look for the first cumulative frequency ≥ 60.
Cumulative at 4 rooms = 68 ≥ 60 → Median = 4 rooms.

Step 3 – Probability of ≥ 5 rooms

Count households with 5 or more rooms:
( 22 + 10 + 12 + 8 = 52 ).

Probability ( = \frac{52}{120} = \frac{13}{30} \approx 0.4333 ) (43.33%).

Answer:

Median = 4 rooms.
Probability (≥ 5 rooms) = ( \frac{13}{30} ) or 43.33 %.

4. Quick Revision Summary

Concept	Quick Check
Frequency Table	List values ↑; sum of freq = total.
Cumulative Frequency	Running sum; use for median/percentile.
Median	Find class where cumulative ≥ ( \frac{N}{2} ).
Percentile	Find class where cumulative ≥ percentile × N; interpolate if needed.
Relative Frequency / Probability	( \frac{f}{N} ).
Contingency Table	Rows × Columns; compute joint probability = cell/N.
Conditional Probability	( P(A
Quick Tips	• Double‑check totals. • Use cumulative