Data Handling – Notes for CBSE Class 7 Maths

Introduction to Data Handling

Data handling is an important part of mathematics that deals with collecting, organizing, and interpreting information (data) to make decisions or draw conclusions. In our daily lives, we come across data in many forms, such as marks in a test, temperatures in a week, or the number of students in a class. This chapter teaches us how to manage and analyze such data effectively.

Key Terms:

• Data: A collection of numbers, facts, or observations gathered for a purpose.
• Raw Data: Data in its original, unorganized form.
• Statistics: The branch of mathematics that deals with collecting, organizing, and interpreting data.

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1. Collection of Data

The first step in data handling is collecting data. Data can be collected through surveys, observations, or experiments. For example, if we want to know the favorite fruit of students in a class, we can ask each student and note their responses.

Example: Suppose we ask 5 students their favorite fruit:

• Student 1: Apple
• Student 2: Banana
• Student 3: Apple
• Student 4: Mango
• Student 5: Banana

This is raw data. It’s unorganized and needs to be arranged for better understanding.

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2. Organization of Data

Once data is collected, it needs to be organized to make sense of it. We can use tables, charts, or diagrams to arrange data systematically.

a) Frequency Distribution Table

A frequency distribution table shows how often (frequency) each item appears in the data.

Example: Using the fruit data above:

Here, “frequency” means the number of times each fruit was chosen.

b) Tally Marks

Tally marks are a quick way to count and record frequencies. We use a vertical line (|) for each item and a diagonal line (/) across four lines to represent 5.

Example: For the same data:

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3. Representation of Data

Organized data can be represented visually using graphs or charts. This makes it easier to understand and compare.

a) Bar Graph

A bar graph uses rectangular bars to represent data. The length or height of each bar shows the frequency of an item.

Example: For the fruit data:

• Draw a horizontal axis (x-axis) and label it “Fruits” (Apple, Banana, Mango).
• Draw a vertical axis (y-axis) and label it “Frequency” (0, 1, 2, 3…).
• Draw bars for Apple (height 2), Banana (height 2), and Mango (height 1).

Key Points:

• Bars should be of equal width.
• There should be equal gaps between bars.

b) Double Bar Graph

A double bar graph compares two sets of data side by side.

Example: Marks of two students in 3 subjects:

• Draw two bars for each subject, one for Student A and one for Student B, with different colors or patterns.

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4. Arithmetic Mean

The arithmetic mean (or average) is a way to find the central value of a data set. It is calculated by adding all the values and dividing by the number of values.

Formula:

Mean=Sum of all observationsNumber of observations\text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}}Mean=Number of observationsSum of all observations​

Example: Marks of 5 students: 70, 80, 65, 90, 75

• Sum = 70 + 80 + 65 + 90 + 75 = 380
• Number of observations = 5
• Mean = 380 ÷ 5 = 76

So, the average mark is 76.

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5. Range

The range tells us how spread out the data is. It is the difference between the highest and lowest values.

Formula:

$$\text{Range}=\text{Highest value}-\text{Lowest value}$$

Example: Using the same marks: 70, 80, 65, 90, 75

• Highest value = 90
• Lowest value = 65
• Range = 90 – 65 = 25

The range is 25.

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6. Mode

The mode is the value that appears most frequently in a data set. A data set can have one mode, more than one mode, or no mode.

Example 1: Data: 3, 5, 5, 7, 8

• 5 appears twice, others appear once.
• Mode = 5

Example 2: Data: 2, 2, 3, 3, 4

• 2 and 3 both appear twice.
• Modes = 2 and 3 (bimodal)

Example 3: Data: 1, 2, 3, 4, 5

• All values appear once.
• No mode.

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7. Median

The median is the middle value of a data set when arranged in ascending or descending order. It divides the data into two equal parts.

Steps to Find Median:

1. Arrange the data in ascending order.
2. If the number of observations (n) is odd, the median is the middle value.
3. If n is even, the median is the average of the two middle values.

Example 1 (Odd number of observations): Data: 10, 20, 30, 40, 50

• Number of observations = 5 (odd)
• Middle value = 30
• Median = 30

Example 2 (Even number of observations): Data: 15, 25, 35, 45

• Number of observations = 4 (even)
• Middle values = 25 and 35
• Median = (25 + 35) ÷ 2 = 60 ÷ 2 = 30

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8. Use of Bar Graphs with a Different Purpose

Bar graphs can also represent data other than frequency, such as averages or totals.

Example: Average monthly rainfall (in mm) in a city:

• Draw a bar graph with “Months” on the x-axis and “Rainfall (mm)” on the y-axis.

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Key Points to Remember

• Data handling helps us make sense of information.
• Frequency tables and tally marks organize raw data.
• Bar graphs visually represent data for easy comparison.
• Mean, mode, and median are measures of central tendency:
  • Mean gives the average.
  • Mode shows the most common value.
  • Median shows the middle value.
• Range measures the spread of data.

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Practice Questions

1. Collect the ages of 10 friends and make a frequency table using tally marks.
2. Draw a bar graph for the following data: Number of books read by 5 students – 3, 5, 2, 4, 1.
3. Find the mean, mode, median, and range of: 12, 15, 12, 18, 20.
4. The heights (in cm) of 6 students are 140, 145, 150, 145, 155, 160. Find the median height.

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Conclusion

Data handling is a practical skill that helps us analyze real-life situations, such as comparing marks, understanding trends, or making decisions. By mastering the concepts of organizing data, calculating averages, and interpreting graphs, we can better understand the world around us. This chapter lays the foundation for more advanced statistical concepts in higher classes.

Chapter 3 Data Handling