RS Aggarwal Class 9 Solutions Chapter-17 Bar Graph, Histogram and Frequency Polygon

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RS Aggarwal Class 9 Solutions Chapter 17 Statistics

Mathematics uses various patterns and shapes to deliver different formulas to structure logic and abstractions. Mathematics has widespread roots in natural science, social science, medicine, finance, and engineering. One of the essential parts of Mathematics is Statistics. Statistics are present as an efficient method to collect, analyze, and visually represent a specific data set. It plays an impactful role in significant scientific discoveries and prediction, analysis, and handling of data. The students often find RS Aggarwal class 9 chapter 17 solution, which defines the complexities of Statistics, to be puzzling. Therefore, to make geometry and statistics clear to the students, we will discuss Graphs, histograms, and Polygon Class 9.

Basics of Statistics

Data

It is defined as facts or figures that are numerical or otherwise collected for a specific purpose.

• Primary data  is data gathered from first-hand sources 

• Secondary data is data was gathered from a source that already had information on hand.

• Ungrouped data is data in its most basic or unprocessed form. The observations are not divided into categories.

• Observations are sorted into groups in grouped data.

• Class Interval is the size of the class into which a particular data is divided.

Bar Graph

Bar graphs are visual representations of organized data in vertical or horizontal rectangular bars, with bar length proportional to data measure. The horizontal axis of the chart shows category data, while the vertical axis represents discrete data. The comparison between two discrete measured values is depicted by a bar graph. It's a representation of the axis that shows a comparison of two separate value categories. To depict particular variables, it is represented by uniform width bars placed with the axis at an identical spacing. The variable is depicted on the base axis, and the height of the bar represents the value. Let's take an example; let's say a student scored 50 in maths, 79 in English, 60 in Science. So, we can represent his overall performance through a bar graph. The base axis, i.e., the x-axis, depicts the student's subjects, while the other axis, i.e., the y-axis, represents his marks in different topics. This is a pictorial representation, which is more convenient to understand.

RS Aggarwal Bar Graph Histogram and Frequency

One of the most used graphs for displaying frequency distribution is the histogram. The frequency distribution, as we all know, determines how frequently each individual value appears in the data set. The histogram resembles the bar graph in appearance, however, there is a distinction between the two. 

A histogram is a form of representation of specific data used in the case of continuous class intervals. It is similar to bar charts and simply represents figures identical to rectangles, with areas equal to the frequency of the given variables and width similar to the class intervals. Let's see how we can construct a histogram –

• First, construct a horizontal line to denote the classes.

• Now, draw even marks on the line corresponding to the class.

• Now, label the marks and name the horizontal axis to prevent any confusion later.

• Now construct a vertical line ending at the lowest class.

• Again label and name the line.

• Now, draw a rectangle on the baseline of heights equal to the frequency of the class.

A histogram is widely used in statistics and carries many concepts that few students struggle to understand. If the students are stuck with the histogram problem, they may refer to RS Aggrawal Bar Graph Histogram and Frequency.

Frequency Polygon

A frequency polygon is constructed when the midpoints of each rectangle in a histogram are connected by line segments. It is possible to draw without using a histogram. Midpoints of class intervals are required. Frequency polygon refers to a particular type of graph used to represent a specific set of data visually. A frequency polygon is drawn by optimizing the data and joining each class interval's midpoints with a line. The heights of these lines highlight the frequencies of the class. Students can initiate a frequency polygon formation from a histogram or calculate the intervals’ midpoints utilizing the frequency distribution table. To calculate the midpoints more precisely, students must add the upper and lower limits of the intervals' boundary values and then divide them by 2.

The midpoint of the polygon =  ( Upper limit + Lower limit)/2

In some cases, students can use a histogram and a frequency polygon at the same time to mix the most accurate result or pictorial representation. Students may learn more about frequency polygon class 9 by consulting the RS Aggarwal Class 9 Maths chapter 17 solution.

Mean, Median, and Mode

• The sum of all the values of all the observations divided by the total number of observations is the mean (or average) of a set of observations.

• The median is the value of a set of observations that divides them into two equal portions. As a result, the median is the score that falls in the middle.

• The mode is the value of an observation that happens the most frequently, i.e., an observation with the highest frequency.

RS Aggarwal Polygon Class 9 Chapter 17 Preparation Tips

• Students must grab the best study material to understand the statistics highlighted in RS Aggarwal Class 9 Maths Chapter 17.

• Students must get a perfect timetable that suits them and supplies the maximum time to revise the complex topics.

• Students must concentrate on developing a base of understanding the concepts rather than jotting them down.

• Students must practice various types of questions, participate in online examinations, and solve the past year’s question papers to explore more problems.

• Students must understand and practice the graphing of linear equations

• Students must know how to arrange data in a natural way. A chart's purpose is to make data easier to understand.