Chapter 16 - Data Handling Revision Notes - Class 7 Mathematics

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📌 Key Points

Data is information collected for a specific purpose.
Primary data is collected directly (surveys, interviews). Secondary data comes from existing sources.
Frequency table organizes raw data by showing how many times each value occurs.
Bar graph: Rectangular bars compare frequencies across categories. All bars have equal width.
Pie chart: Circular sectors show parts of a whole. Angle = (frequency÷total)×360°
Mean (Average): Sum of all values divided by number of values.
Median: Middle value when data arranged in order. For even count: average of two middle values.
Mode: Value that appears most frequently. Data can have one mode, multiple modes, or no mode.
Range: Difference between maximum and minimum values. Shows how spread out the data is.
Probability: Likelihood of event = (favorable outcomes)÷(total outcomes). Always between 0 and 1.
Certain event has probability 1. Impossible event has probability 0.
Theoretical probability is based on mathematics. Experimental is based on actual trials.
For even number of values in median calculation, take average of two middle numbers.
In pie chart: All angles sum to 360°. Convert angle to percentage: (angle÷360)×100
When comparing datasets, use mean for average, median for typical value, mode for most common.

📘 Important Definitions

Data

Information collected for analysis, either quantitative (numbers) or qualitative (descriptions).

Frequency

Number of times a value or category appears in a dataset.

Mean

The average value found by summing all values and dividing by the count of values.

Median

The middle value when data is arranged in ascending or descending order.

Mode

The value that appears most frequently in a dataset.

Range

The difference between the maximum and minimum values in a dataset.

Probability

The measure of likelihood that an event will occur, expressed as a number between 0 and 1.

Primary Data

Data collected directly from the source through surveys, observations, or experiments.

🔢 Formulas & Laws

Mean

Mean = (Sum of all values) ÷ (Number of values)

Also called average

Range

Range = Maximum value - Minimum value

Measures spread of data

Pie Chart Angle

Angle = (Frequency ÷ Total) × 360°

Sum of all angles = 360°

Percentage from Angle

Percentage = (Angle ÷ 360) × 100

Converts pie chart angle to percentage

Probability

P(Event) = (Number of favorable outcomes) ÷ (Total number of possible outcomes)

0 ≤ P(Event) ≤ 1

⚠️ Common Mistakes

✗ Wrong: Calculating mean without finding the sum first or dividing by wrong count.

✓ Correct: Always sum all values first, then divide by the exact count of values.

✗ Wrong: Finding median without arranging data in order first.

✓ Correct: Always arrange data in ascending order before finding the median.

✗ Wrong: Using 180° instead of 360° for full circle in pie chart calculations.

✓ Correct: A complete circle is 360°. Angle = (frequency÷total)×360°

✗ Wrong: Forgetting to average the two middle values for even number of data points in median.

✓ Correct: For even count, median = (value1 + value2)÷2 where value1 and value2 are the two middle values.

✗ Wrong: Calculating probability greater than 1 or less than 0.

✓ Correct: Probability is always between 0 and 1. If you get >1 or <0, recheck your calculation.

📝 Exam Focus

These questions are frequently asked in CBSE exams:

Calculating mean, median, mode from given data

2m★★★

Creating frequency tables and drawing bar graphs

3m★★★

Pie chart: calculating angles and drawing

3m★★

Finding range and interpreting data spread

1m★★

Basic probability problems with coins, dice, cards

2m★★

Word problems involving data interpretation

🎯 Last-Minute Recall