Data Handling

Overview

Data Handling is a foundational topic in the KTET Mathematics syllabus that tests your ability to organise, represent, and interpret numerical information. This topic bridges arithmetic skills with real-world applications—understanding survey results, classroom performance data, or population statistics.

For KTET, expect questions that ask you to read values from graphs, calculate central tendency measures (mean, median, mode), or identify the most appropriate representation for given data. Questions typically combine computational accuracy with conceptual understanding—you must know not just *how* to calculate the mean, but *when* mean is appropriate versus median.

Mastery requires two distinct skills: visual literacy (extracting information from tables and graphs) and statistical calculation (computing averages correctly). Both appear frequently in Category I, II, and III papers.

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Key Concepts

• **Data** is a collection of facts, numbers, or observations gathered for analysis. Raw data is unorganised; organised data is arranged systematically in tables or arrays.

• **Frequency** tells how many times a particular value or category appears. A frequency distribution table groups data and shows the count for each group.

• **Range** is the difference between the highest and lowest values in a dataset. Range = Maximum value − Minimum value.

• **Pictographs** use pictures or symbols to represent data, where each symbol stands for a fixed number of items. Always check the key/legend.

• **Bar graphs** use rectangular bars of equal width; the height (or length) of each bar represents the frequency or value. Bars do not touch each other.

• **Mean** is the arithmetic average—it uses every data point and is sensitive to extreme values (outliers).

• **Median** is the middle value when data is arranged in order—it is resistant to outliers and useful for skewed distributions.

• **Mode** is the most frequently occurring value—a dataset can have no mode, one mode, or multiple modes.

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Formulas / Key Facts

**Mean (Arithmetic Average)** Mean = Sum of all observations ÷ Number of observations Mean = Σx ÷ n

**Median**

• Arrange data in ascending or descending 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** Mode = the value that appears most frequently (No formula—simply count occurrences)

**Range** Range = Highest value − Lowest value

**Reading Pictographs** Total count = Number of symbols × Value per symbol

**Bar Graph Rules**

• Equal width bars
• Equal spacing between bars
• Scale must start from zero (or clearly indicate a break)

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Worked Examples

### Example 1: Calculating Mean **Problem:** Find the mean of: 12, 15, 18, 21, 24

**Solution:** Step 1: Add all values 12 + 15 + 18 + 21 + 24 = 90

Step 2: Count the observations n = 5

Step 3: Divide Mean = 90 ÷ 5 = 18

**Answer:** Mean = 18

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### Example 2: Finding Median **Problem:** Find the median of: 7, 3, 9, 5, 11, 2, 8

**Solution:** Step 1: Arrange in ascending order 2, 3, 5, 7, 8, 9, 11

Step 2: Count observations n = 7 (odd)

Step 3: Find middle position Position = (7 + 1) ÷ 2 = 4th value

Step 4: Identify the 4th value 2, 3, 5, **7**, 8, 9, 11

**Answer:** Median = 7

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### Example 3: Finding Median (Even Count) **Problem:** Find the median of: 4, 8, 12, 16, 20, 24

**Solution:** Data is already in order. n = 6 (even)

Middle positions: 6 ÷ 2 = 3rd and 4th values 3rd value = 12, 4th value = 16

Median = (12 + 16) ÷ 2 = 28 ÷ 2 = 14

**Answer:** Median = 14

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### Example 4: Reading a Pictograph **Problem:** A pictograph shows book sales where each symbol represents 10 books.

• Monday: ☐☐☐
• Tuesday: ☐☐☐☐☐

How many more books were sold on Tuesday than Monday?

**Solution:** Monday sales = 3 × 10 = 30 books Tuesday sales = 5 × 10 = 50 books Difference = 50 − 30 = 20 books

**Answer:** 20 more books sold on Tuesday

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### Example 5: Finding Mode **Problem:** Find the mode of: 5, 8, 6, 8, 9, 8, 5, 6, 8

**Solution:** Count each value:

• 5 appears 2 times
• 6 appears 2 times
• 8 appears 4 times
• 9 appears 1 time

8 appears most frequently.

**Answer:** Mode = 8

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Common Mistakes

**Mistake 1: Forgetting to arrange data before finding median** Wrong: Finding the middle value from unordered data. Fix: Always sort data in ascending or descending order first, then locate the middle position.

**Mistake 2: Confusing when to use mean versus median** Wrong: Using mean when data has extreme outliers (e.g., incomes of 10, 12, 15, 11, 500). Fix: Use median for skewed data with outliers; mean gets distorted by extreme values.

**Mistake 3: Misreading the pictograph key** Wrong: Counting symbols directly without checking what each symbol represents. Fix: Always multiply the number of symbols by the value given in the key/legend.

**Mistake 4: Saying "no mode" when all values appear equally** Wrong: Claiming any value as mode when each appears the same number of times. Fix: If all values have equal frequency, the dataset has no mode.

**Mistake 5: Errors in median position formula** Wrong: For n = 7, using position 7 ÷ 2 = 3.5. Fix: For odd n, use (n + 1) ÷ 2. So (7 + 1) ÷ 2 = 4th position.

**Mistake 6: Bar graph scale misreading** Wrong: Estimating bar height without checking the scale intervals. Fix: Carefully read the y-axis scale; note whether intervals are 5, 10, 20, etc.

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Quick Reference

• Mean = Sum ÷ Count (affected by outliers)
• Median = Middle value after sorting (resistant to outliers)
• Mode = Most frequent value (can be none, one, or many)
• Range = Maximum − Minimum
• Pictograph: Count symbols × Value per symbol
• Bar graphs: Height = frequency; bars never touch