Statistics and Data Handling forms a crucial component of the upper-primary mathematics curriculum and appears consistently in WB TET Paper II. This topic tests your ability to organise raw data, calculate measures of central tendency (mean, median, mode), and interpret graphical representations such as bar graphs, histograms, pie charts and frequency polygons.
For the TET examination, you must demonstrate both computational proficiency and pedagogical understanding. Questions typically involve calculating averages from grouped or ungrouped data, identifying the correct graph type for given data, and interpreting visual representations. Since this topic connects mathematics with real-world applications—census data, weather patterns, classroom attendance—it is ideal for activity-based teaching, making it a favourite area for pedagogy-linked questions.
Mastery here requires understanding when to use each measure of central tendency, recognising their limitations, and knowing how to represent data visually for maximum clarity.
Key Concepts
**Data** refers to facts or figures collected for analysis. It can be primary (collected firsthand) or secondary (obtained from existing sources).
**Raw data** is unorganised information; when arranged systematically using tally marks or frequency tables, it becomes **organised data**.
**Frequency** is the number of times a particular observation occurs in a dataset.
**Mean (Arithmetic Average)** is the sum of all observations divided by the total number of observations—best used when data has no extreme outliers.
**Median** is the middle value when data is arranged in ascending or descending order—preferred when data contains extreme values.
**Mode** is the most frequently occurring observation—useful for categorical data like favourite colours or shoe sizes.
**Range** is the difference between the highest and lowest values, indicating the spread of data.
**Class interval** is a group of values in grouped data (e.g., 10–20, 20–30), with **class mark** being the midpoint of each interval.
Formulas / Key Facts
**Mean (Ungrouped Data)** Mean = Sum of all observations ÷ Number of observations Mean = Σx ÷ n
**Mean (Grouped Data — Direct Method)** Mean = Σ(f × x) ÷ Σf where f = frequency, x = class mark (midpoint of class interval)
**Median (Ungrouped Data)**
Arrange data in ascending order
If n is odd: Median = value at position (n + 1) ÷ 2
If n is even: Median = average of values at positions n ÷ 2 and (n ÷ 2) + 1
**Mode (Ungrouped Data)** Mode = observation with highest frequency A dataset can have no mode, one mode (unimodal), or multiple modes (bimodal/multimodal).
**Range** Range = Maximum value − Minimum value
**Class Mark (Midpoint)** Class mark = (Lower limit + Upper limit) ÷ 2
Worked Examples
**Example 1: Finding Mean** The marks of 5 students are: 45, 52, 60, 48, 55. Find the mean.
Solution: Sum = 45 + 52 + 60 + 48 + 55 = 260 Number of observations = 5 Mean = 260 ÷ 5 = **52 marks**
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**Example 2: Finding Median** Find the median of: 12, 7, 19, 5, 23, 11, 15
Solution: Arrange in ascending order: 5, 7, 11, 12, 15, 19, 23 Number of observations (n) = 7 (odd) Median position = (7 + 1) ÷ 2 = 4th position Median = **12**
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**Example 3: Finding Mean from Grouped Data**
| Class Interval | Frequency (f) | Class Mark (x) | f × x | |----------------|---------------|----------------|-------| | 0–10 | 3 | 5 | 15 | | 10–20 | 5 | 15 | 75 | | 20–30 | 7 | 25 | 175 | | 30–40 | 5 | 35 | 175 |
**Example 4: Reading a Bar Graph** A bar graph shows books read by students: Rani (8 books), Suman (5 books), Amit (10 books), Priya (7 books). Who read the most books? What is the total?
Solution: Most books read by: **Amit (10 books)** Total = 8 + 5 + 10 + 7 = **30 books**
Common Mistakes
**Confusing mean with median** → Mean uses all values in calculation; median only considers the middle position. Use median when extreme values exist (e.g., one student scoring 100 when others score 30–40).
**Forgetting to arrange data before finding median** → Always sort data in ascending or descending order first. Finding the "middle" of unsorted data gives wrong answers.
**Using wrong class mark in grouped data** → Students sometimes use the lower or upper limit instead of the midpoint. Always calculate: (Lower + Upper) ÷ 2.
**Claiming "no mode" when all values appear once** → This is actually correct. A dataset where every value occurs exactly once has no mode—don't force an answer.
**Misreading graph scales** → In bar graphs and histograms, check the scale on the y-axis carefully. If each unit represents 5 students, a bar reaching 4 units means 20 students, not 4.
**Confusing histogram with bar graph** → Histograms show continuous data with no gaps between bars; bar graphs show discrete categories with gaps between bars.
Graphical Representations — Quick Guide
| Graph Type | Use For | Key Feature | |------------|---------|-------------| | Pictograph | Simple data for young learners | Uses pictures/symbols | | Bar Graph | Comparing discrete categories | Bars with equal gaps | | Histogram | Continuous grouped data | Bars touch each other | | Pie Chart | Showing parts of a whole | Circle divided into sectors | | Frequency Polygon | Trends in grouped data | Line connecting class-mark points | | Line Graph | Changes over time | Points connected by lines |
Quick Reference
Mean is sensitive to extreme values; median and mode are not.
For ungrouped data with n values: median position = (n + 1) ÷ 2 when n is odd.
Class mark = (Lower limit + Upper limit) ÷ 2 — always use this for grouped-data mean.
Histogram bars touch; bar graph bars have gaps.
Mode is the only measure applicable to non-numerical (categorical) data.
Range = Maximum − Minimum; it measures spread, not central tendency.
You read the notes — now try one
The marks obtained by 8 students in a test are: 15, 18, 20, 22, 22, 25, 28, 30. What is the median of these marks?
Tap an option to check your answer.
👥 Study this together
Invite your prep group — read the same notes, then discuss doubts in this topic's shared room.
The marks obtained by 8 students in a test are: 15, 18, 20, 22, 22, 25, 28, 30. What is the median of these marks?
Q2 · Statistics and Data Handling · EASY
The number of books read by 10 students during summer vacation are: 3, 5, 7, 5, 8, 5, 9, 6, 5, 7. What is the mode of this data?
Q3 · Statistics and Data Handling · MEDIUM
The daily wages (in rupees) of 6 workers are: 250, 300, 280, 320, 300, 350. Find the mean wage.
Q4 · Statistics and Data Handling · HARD
A teacher recorded the marks of 9 students: 45, 50, 55, 60, 65, 70, 75, 80, 85. One more student joins and scores 40 marks. What is the change in the median after the new student's marks are included?
Q5 · Statistics and Data Handling · EASY
The marks obtained by 7 students are: 12, 15, 18, 14, 16, 20, 17. What is the median of this data?