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Chapter Analysis
Intermediate15 pages • EnglishQuick Summary
This chapter on statistics for Class 9 delves into the graphical representation of data, focusing on bar graphs, histograms, and frequency polygons. It emphasizes the importance of visual data representation to simplify comparisons and provide a clearer understanding than numerical tables. The chapter includes practical examples and exercises to illustrate these concepts and their application in real-life scenarios, such as analyzing the number of students born in different months or assessing test performances. Ultimately, the chapter aims to develop skills in interpreting graphical data and drawing meaningful conclusions.
Key Topics
- •Graphical Representation of Data
- •Bar Graphs
- •Histograms
- •Frequency Polygons
- •Comparing Graphical Data
- •Interpreting Data from Graphs
Learning Objectives
- ✓Understand different forms of data representation.
- ✓Interpret and analyze data using bar graphs, histograms, and frequency polygons.
- ✓Distinguish between categorical and continuous data.
- ✓Draw and interpret histograms and frequency polygons.
- ✓Apply graphical representations to solve real-world data problems.
Questions in Chapter
A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %): 1. Reproductive health conditions 31.8 2. Neuropsychiatric conditions 25.4 3. Injuries 12.4 4. Cardiovascular conditions 4.3 5. Respiratory conditions 4.1 6. Other causes 22.0 (i) Represent the information given above graphically. (ii) Which condition is the major cause of women’s ill health and death worldwide? (iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.
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The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below. Section Number of girls per thousand boys Scheduled Caste (SC) 940 Scheduled Tribe (ST) 970 Non SC/ST 920 Backward districts 950 Non-backward districts 920 Rural 930 Urban 910 (i) Represent the information above by a bar graph. (ii) In the classroom discuss what conclusions can be arrived at from the graph.
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Given below are the seats won by different political parties in the polling outcome of a state assembly elections: Political Party A B C D E F Seats Won 75 55 37 29 10 37 (i) Draw a bar graph to represent the polling results. (ii) Which political party won the maximum number of seats?
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Additional Practice Questions
If a histogram represents the distribution of a dataset, describe how the shape of the histogram can provide information about the dataset?
mediumAnswer: The shape of a histogram can reveal the distribution's characteristics. A symmetrical shape indicates a normal distribution, while a skewed shape shows data skewing to the left or right. A uniform shape suggests even frequency of data across intervals and a multi-modal shape indicates multiple peaks.
What is the difference between a bar graph and a histogram?
mediumAnswer: A bar graph represents categorical data with rectangular bars with heights or lengths proportional to the values they represent. In contrast, a histogram represents continuous data and the bars touch each other, indicating data intervals. Bar graphs are used for discrete data, whereas histograms represent frequency distributions of continuous data.
How can a frequency polygon be drawn from a histogram?
easyAnswer: To draw a frequency polygon from a histogram, plot points at the mid-points of the top of each bar and connect these points with straight lines. Extend the lines to the x-axis at the beginning and end of the graph to complete the polygon.
Explain the utility of using a frequency polygon instead of a histogram.
mediumAnswer: A frequency polygon allows for easier comparison of two or more distributions, especially when they are overlaid. It provides a clearer view of the data trends and fluctuations than a histogram by highlighting the shape of the data distribution.
Create a bar graph that represents data for monthly rainfall in a city where January has 80mm, February 50mm, March 70mm, April 60mm, and May 90mm.
easyAnswer: To create the bar graph, draw the x-axis to represent the months and the y-axis for rainfall in mm. Plot bars for each month according to their rainfall: January (80mm), February (50mm), March (70mm), April (60mm), and May (90mm). Ensure bars are equally spaced.