Data Handling

Overview

Data Handling is a foundational topic in the TN TET Mathematics section that tests your ability to organise, represent and interpret numerical information. This topic bridges arithmetic skills with real-world application—exactly the kind of practical mathematics primary teachers must convey to young learners.

For TN TET, expect questions on reading and constructing tables, bar graphs and pictographs, plus calculating measures of central tendency (mean, median, mode). The pedagogy portion may also ask how to teach data interpretation to children using activity-based methods. Mastering this topic requires both computational accuracy and the ability to extract meaning from visual data representations.

Students must be comfortable with quick mental arithmetic for mean calculations, arranging data for median, and spotting the most frequent value for mode. Graph-reading questions often test whether you can extract specific values or compare categories—skills that appear deceptively simple but trip up candidates who rush.

Key Concepts

• **Data** is a collection of facts, numbers or observations gathered for analysis. Raw data becomes meaningful only after organisation.

• **Frequency** tells how many times a particular value or category appears in a dataset. A frequency table organises data by listing each value alongside its frequency.

• **Pictograph** uses symbols or pictures to represent data, where each symbol stands for a fixed number of items (called the key or scale).

• **Bar graph** uses rectangular bars of equal width to represent data. Bar height (or length) shows the value; bars do not touch each other.

• **Mean** (arithmetic average) = Sum of all observations ÷ Number of observations. It considers every data point.

• **Median** is the middle value when data is arranged in ascending or descending order. For an even number of observations, median = average of the two middle values.

• **Mode** is the observation that occurs most frequently. A dataset can have no mode, one mode, or multiple modes.

• **Range** = Highest value − Lowest value. It measures the spread of data.

Formulas / Key Facts

**Mean** Mean = (Sum of all observations) ÷ (Total number of observations) Mean = Σx ÷ n

**Median**

• Arrange data in ascending order first.
• 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** Mode = the value with the highest frequency (no formula—identify by counting).

**Range** Range = Maximum value − Minimum value

**Pictograph key**: Always check the scale. If one symbol = 5 units and you see 3 symbols, the value is 15.

**Bar graph reading**: Read the scale on the y-axis carefully. If the scale starts at a number other than zero, adjust your interpretation.

**Relationship insight**: For a symmetric dataset, mean ≈ median. If the data is skewed, mean gets pulled toward extreme values while median stays robust.

Worked Examples

### Example 1: Calculating Mean **Problem**: The marks obtained by 5 students are 72, 85, 90, 68 and 75. Find the mean.

**Solution**: Step 1: Sum of marks = 72 + 85 + 90 + 68 + 75 = 390 Step 2: Number of students = 5 Step 3: Mean = 390 ÷ 5 = **78**

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### Example 2: Finding Median **Problem**: Find the median of 14, 9, 21, 18, 13, 17, 20.

**Solution**: Step 1: Arrange in ascending order: 9, 13, 14, 17, 18, 20, 21 Step 2: Number of observations n = 7 (odd) Step 3: Middle position = (7 + 1) ÷ 2 = 4th position Step 4: The 4th value is **17**. Median = **17**

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### Example 3: Median with Even Number of Values **Problem**: Find the median of 5, 8, 12, 15, 18, 22.

**Solution**: Step 1: Data is already arranged. n = 6 (even) Step 2: Middle positions = 6 ÷ 2 = 3rd and 4th positions Step 3: Values at 3rd and 4th positions = 12 and 15 Step 4: Median = (12 + 15) ÷ 2 = **13.5**

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### Example 4: Reading a Pictograph **Problem**: In a pictograph showing books read by students, each book symbol = 4 books. Ravi's row shows 6 symbols. How many books did Ravi read?

**Solution**: Books read = 6 × 4 = **24 books**

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### Example 5: Finding Mode **Problem**: Find the mode of 3, 7, 5, 3, 9, 3, 7, 5, 3.

**Solution**: Count frequencies: 3 appears 4 times, 7 appears 2 times, 5 appears 2 times, 9 appears 1 time. Highest frequency = 4 (for value 3) Mode = **3**

Common Mistakes

• **Forgetting to arrange data before finding median** → Always sort the data in ascending order first. Picking the "middle" from unsorted data gives wrong answers.

• **Confusing the pictograph scale** → Students assume each symbol = 1. Always read the key. If symbol = 10 and there are 3.5 symbols, the value is 35, not 3.5.

• **Adding frequencies instead of values when calculating mean** → Mean uses the actual data values, not how many times they appear. If 5 appears 3 times, add 5 + 5 + 5, not 5 + 3.

• **Declaring "no mode" too quickly** → If all values appear equally often, there is no mode. But if two or more values share the highest frequency, all of them are modes (bimodal or multimodal).

• **Misreading bar graph scales** → When the y-axis scale jumps by 10s or 20s, students sometimes read between lines incorrectly. Trace horizontally from bar top to axis carefully.

Quick Reference

• Mean = Total sum ÷ Number of items (uses all values)
• Median = Middle value after sorting (for even n, average the two middle values)
• Mode = Most frequent value (can be more than one)
• Range = Highest − Lowest
• Pictograph: Value = Number of symbols × Scale
• Bar graph bars have equal width and do not touch