Data Interpretation & Statistics — CUET UG General Test

This is the smallest of the five Quantitative & Numerical Ability topics, but it rewards careful reading more than any of the others: every question starts from a single small table, and the entire difficulty lies in extracting the right numbers from it accurately — the calculation that follows is always basic. A single misread cell produces a confidently wrong answer built on otherwise-correct arithmetic.

1. Reading a table: maximum, minimum, total and share

Before calculating anything, scan the whole table once to identify its rows, columns and units — a table's maximum or minimum value is found by direct comparison, never by any calculation, and the total is simply the sum of every relevant entry. A "share of total" or "part of a group" question then divides one entry by that total, exactly like the percentage-of-a-group questions from the Arithmetic chapter.

2. Mean (average) and finding a missing value

The mean of a dataset is its sum divided by its count — identical to "average" elsewhere in this cluster — and a "missing value" question reverses that relationship: multiply the given mean by the total count to recover the full sum, then subtract the sum of the known values to isolate the missing one.

3. Median

The median is the middle value of a dataset once every value is arranged in order — for an ODD count of values, it is the single middle value directly; for an EVEN count, it is the average of the two middle values. Arranging the data in order first is not optional: a median taken from unsorted data is simply wrong, regardless of how the calculation afterward is done.

$\{3,7,9,12,18\}$ (5 values, odd) has median 9 directly. $\{4,8,15,16,23,42\}$ (6 values, even) has median $\frac{15+16}{2}=15.5$.

4. Mode

The mode is the value that occurs most frequently in a dataset — unlike mean and median, it does not require sorting or arithmetic, only counting how many times each value appears. A dataset can have one mode, more than one (if two or more values tie for the highest frequency), or no mode at all (if every value occurs equally often).

5. Range

The range is simply the maximum value minus the minimum value in a dataset — the single fastest statistic to compute, since it needs only two values already identified while reading the table.

$\text{Range}=\text{Maximum}-\text{Minimum}$

6. Combined mean of two groups

Exactly as with combined averages elsewhere in this cluster, the combined mean of two groups is their combined sum divided by their combined count — never the simple average of the two individual means, unless both groups happen to be the same size.

$\text{Combined mean}=\frac{n_1{\bar{x}}_1+n_2{\bar{x}}_2}{n_1+n_2}$

7. Percentage change and identifying the highest-growth period

Percentage change between two consecutive periods in a table follows the same formula as any percentage increase — (new value minus old value), divided by the OLD value, times 100 — computed separately for every pair of consecutive periods when a question asks which period had the highest growth.

A larger absolute increase does NOT automatically mean a higher percentage growth — a small absolute increase on a small base can outpace a larger absolute increase on a much larger base, so every candidate period's percentage must actually be computed and compared, not estimated by eye.

Worked Examples

A company's yearly sales (in ₹ lakh) are given below.

Example 1. Find the total sales across all five years.

$120+150+135+180+165=750$.

Answer: ₹750 lakh.

Example 2. In which year were sales the highest, and by how much do they exceed the lowest year's sales?

Highest: 2022 (₹180 lakh). Lowest: 2019 (₹120 lakh). Difference $=180-120=60$.

Answer: 2022 is highest; it exceeds 2019 by ₹60 lakh.

Example 3. What percentage of the 5-year total do 2022's sales represent?

$\frac{180}{750}\times 100=24\%$.

Answer: 24%.

Example 4. Find the mean, median and mode of: $12,15,18,21,24$.

Mean $=\frac{12+15+18+21+24}{5}=\frac{90}{5}=18$. Median (already sorted, odd count) $=18$ (the middle value). No value repeats, so there is no mode.

Answer: Mean = 18, Median = 18, Mode = none.

Example 5. Find the median of: $7,12,3,18,9$.

Sorted: $3,7,9,12,18$ (5 values, odd count). The middle value is 9.

Answer: 9.

Example 6. Find the median of: $4,8,15,16,23,42$.

Already sorted, 6 values (even count). Median $=\frac{15+16}{2}=15.5$.

Answer: 15.5.

Example 7. Find the mode of: $2,3,3,5,7,3,8$.

3 appears three times, more than any other value.

Answer: 3.

Example 8. Find the range of: $12,45,7,89,34$.

Maximum $=89$, minimum $=7$. Range $=89-7=82$.

Answer: 82.

Example 9. One group of 5 numbers has a mean of 20; another group of 3 numbers has a mean of 30. Find the combined mean of all 8 numbers.

Combined sum $=5(20)+3(30)=100+90=190$. Combined mean $=\frac{190}{8}=23.75$.

Answer: 23.75.

Example 10. The mean of 5 numbers is 20. Four of the numbers are 15, 22, 18 and 25. Find the fifth number.

Total sum $=20\times 5=100$. Sum of the four known numbers $=15+22+18+25=80$. Fifth number $=100-80=20$.

Answer: 20.

Example 11. Using the sales table above, find the percentage change in sales for each year from 2019 to 2023, and identify the year of highest growth.

2020: $\frac{150-120}{120}\times 100=25\%$. 2021: $\frac{135-150}{150}\times 100=-10\%$. 2022: $\frac{180-135}{135}\times 100\approx 33.3\%$. 2023: $\frac{165-180}{180}\times 100\approx -8.3\%$.

Answer: 2022 has the highest growth, at approximately 33.3% — even though 2020's absolute increase (₹30 lakh) is smaller than 2022's (₹45 lakh) in raw terms, both years' PERCENTAGE growth had to be computed and compared directly, and 2022's percentage growth on its 2021 base turns out highest.

Summary

Every question in this topic starts with reading a table correctly — maximum, minimum and total are found by direct comparison or summation, never by calculation shortcuts, and a misread cell produces a wrong answer regardless of correct arithmetic afterward.

Mean = sum / count, reversible to recover a sum or a missing value. Median requires sorting first — the single middle value for an odd count, the average of the two middle values for an even count. Mode is the most frequent value, found by counting, not calculating. Range = maximum − minimum, the fastest statistic to compute.

A combined mean of two groups is their combined sum over combined count, never the simple average of two means unless the groups are equal size. Percentage change between periods must be computed separately for every candidate period when identifying the highest-growth period — a larger absolute increase does not guarantee a higher percentage increase.