Data Handling
Overview
Data Handling is about collecting, organising, and understanding information called data. We learn to record data using tally marks, represent it in tables, draw pictographs and bar graphs, and find the average (mean) of a set of numbers. These skills help us read and compare information easily in daily life, such as favourite sports, marks scored, or weather records. By the end of this chapter, students can interpret and present data in a clear and meaningful way.
Typed Notes
Collecting and Organising Data
Data means information collected in the form of numbers or facts. Raw data is unorganised and hard to read. We organise it using a tally marks table. For example, if we record the favourite fruit of 20 students, we put a tally mark for each student next to the fruit they choose. After every four marks we draw a diagonal line across them to make a group of five. Counting these groups gives us the frequency, which is how many times each item appears. This organised table is called a frequency distribution table.
Pictograph
A pictograph represents data using pictures or symbols. Each symbol stands for a fixed number of items, called the scale. For example, one apple symbol may represent 5 students. To show 15 students we draw 3 apple symbols. To show 10 students we draw 2 symbols. Always include a key that explains what one symbol means. Pictographs make it easy to compare data at a glance. However, when numbers are large or unequal, drawing exact half or quarter symbols can be tricky, which is a limitation of pictographs.
Bar Graph
A bar graph uses solid rectangular bars to show data. All bars have the same width and are drawn on a graph with two axes. The horizontal axis (x-axis) shows the categories, such as names of subjects or days. The vertical axis (y-axis) shows the numbers or values. The height of each bar equals the value it represents. A uniform scale is chosen for the y-axis, for example each unit = 5 students. Bar graphs are better than pictographs for large numbers because we can read exact values easily and compare bars quickly by looking at their heights.
Arithmetic Mean (Average)
The arithmetic mean helps us find a single value that represents an entire group of numbers. It is calculated by adding all the observations together and then dividing by the total number of observations. Formula: Mean = Sum of observations ÷ Number of observations. For example, if a student scores 10, 14, 12, and 16 in four tests, the mean = (10+14+12+16) ÷ 4 = 52 ÷ 4 = 13. The mean is always between the smallest and the largest value in the data. It gives a fair idea of the overall performance or quantity.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Data is a collection of numbers or facts gathered for a specific purpose.
- 02Tally marks are used to count and organise data quickly; every fifth tally crosses the previous four.
- 03A pictograph uses pictures or symbols to represent data, where each symbol stands for a fixed number.
- 04A bar graph uses rectangular bars of equal width; the height of each bar shows the value of that item.
- 05The arithmetic mean (average) = Sum of all observations ÷ Number of observations.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
The marks scored by 5 students in a test are 8, 12, 10, 14, and 6. Find the arithmetic mean of their marks.
In a pictograph, one symbol of a book represents 4 students. If the row for 'Science' shows 5 book symbols, how many students like Science?
A bar graph has a scale where 1 unit on the y-axis = 5 students. A bar for 'Cricket' reaches up to 8 units. How many students like Cricket?
The number of books read by Priya in 4 months are 3, 5, 4, and 8. Find the mean number of books read per month.
Draw a tally marks table for the following data of favourite colours chosen by 10 students: Red, Blue, Red, Green, Blue, Red, Blue, Green, Red, Blue.
Data Handling teaches us to collect raw data, organise it with tally marks, and display it using pictographs or bar graphs for easy comparison. A pictograph uses symbols with a key, while a bar graph uses bars on two axes. The arithmetic mean, found by dividing the total sum by the number of items, gives a single representative value for the whole data set. These tools are widely used in everyday life.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What does the mean of a set of numbers represent?
Q2.In a tally marks table, how is the number 5 represented?
Q3.A pictograph uses one star symbol to represent 10 items. How many symbols are needed to show 40 items?
Q4.Which axis of a bar graph usually shows the categories or names?
Mark karo — dashboard par progress dikhega.