Data Handling
Overview
Data Handling is the process of collecting, organising, and interpreting numerical information to draw meaningful conclusions. In Class 7, students learn to find averages (mean, median, mode), understand range, represent data using bar graphs and histograms, and read pie charts. These tools help us make sense of large amounts of information in everyday life, from cricket scores to class marks and weather records.
Typed Notes
Measures of Central Tendency: Mean, Median and Mode
Mean is calculated by dividing the sum of all observations by the total number of observations. It gives a single value representing the entire data. Median is the middle value when data is arranged in ascending order. For an odd number of values, the median is the exact middle term. For an even number, it is the average of the two middle terms. Mode is the value that appears most often. These three measures help us understand where the 'centre' of the data lies and are called measures of central tendency.
Range and Grouped Data
Range tells us how spread out the data is. It is found by subtracting the smallest value from the largest value. When data is very large, we group it into class intervals such as 0–10, 10–20, 20–30, and so on. The number of observations falling in each class is called the frequency. A frequency distribution table organises this grouped data neatly. The class mark or mid-point of each interval is used to represent all values in that class and is calculated as the average of the upper and lower class limits.
Bar Graphs and Histograms
A bar graph uses separate rectangular bars to represent individual categories of data, with gaps between bars. The height of each bar shows the frequency or value. A histogram is used for continuous grouped data and looks similar to a bar graph but the bars touch each other with no gaps, showing that the data is continuous. The horizontal axis shows class intervals and the vertical axis shows frequency. Histograms are useful when data is large and needs to be grouped, such as marks of students or heights of people in a group.
Pie Charts (Circle Graphs)
A pie chart is a circular graph divided into sectors, where each sector represents a part of the whole data. The entire circle represents 360°, which equals 100% of the data. To find the central angle for each component, we use the formula: (Value of component ÷ Total value) × 360°. Pie charts make it easy to compare parts of a whole visually. For example, if a family spends ₹3000 on food out of a total monthly expense of ₹12000, the central angle for food = (3000 ÷ 12000) × 360° = 90°.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Mean is the arithmetic average; it is affected by every value in the data set including extreme values.
- 02Median is the middle value of ordered data and is not affected by extreme values; it is a better measure when data has outliers.
- 03Mode is the most frequently occurring value; a data set can have more than one mode or no mode at all.
- 04A histogram looks like a bar graph but has no gaps between bars because it represents continuous class intervals of grouped data.
- 05In a pie chart, each sector's central angle represents a component's share of the total, and all angles add up to 360°.
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
The marks scored by 7 students in a test are: 45, 52, 38, 60, 52, 47, 52. Find the mean, median, and mode.
The ages of 8 members of a club are: 12, 15, 14, 18, 12, 16, 14, 13. Find the range and median.
A family's monthly expenses are: Food ₹4500, Rent ₹3000, Education ₹1500, Others ₹1000. Total = ₹10000. Find the central angle for each component to draw a pie chart.
The following data shows the number of hours 6 students studied in a week: 5, 8, 6, 10, 8, 7. Find the mean number of hours studied.
Find the class mark of the class intervals 20–30, 30–40, and 40–50.
Data Handling involves collecting and organising data to find useful information. Mean, median, and mode are the three measures of central tendency. Range measures the spread of data. Large data is grouped into class intervals and shown using frequency tables, histograms, and bar graphs. Pie charts show each component as a fraction of the whole using sectors of a circle. Together, these tools help us analyse and interpret real-life data effectively.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What is the mode of the data: 3, 5, 7, 5, 9, 5, 3?
Q2.The median of the data 11, 13, 15, 17, 19 is:
Q3.In a pie chart, a component has a value of 90 out of a total of 360. What is its central angle?
Q4.Which of the following graphs is used to represent continuous grouped data with no gaps between bars?
Mark karo — dashboard par progress dikhega.