ICSE Class 10 Maths Chapter 27 Graphical Representation of Statistical Data

Unit 7: Statistics

Chapter 27: Graphical Representation of Statistical Data

Points to Remember

1. Graphical Representation of Data

The tabular representation of data is an ideal way of presenting them in a systematic manner. When these numerical figures are represented pictorially or graphically they become more noticeable and easily intelligible. With the help of these pictures or graphs, data can be compared easily.

In this chapter, we shall deal with three types of graphs, namely:

(i) Histogram (ii) Frequency Polygon (iii) Cumulative Frequency Curve or Ogive.

(A) Histogram

A histogram is a graphical representation of a frequency distribution in an exclusive form (i.e. in continuous form), in the form of rectangles with class-intervals as bases and the corresponding frequencies as heights, there being no gap between any two successive rectangles.

Method of Drawing a Histogram

Step 1. If the given frequency distribution is in inclusive form, convert it into an exclusive form.

Step 2. Taking suitable scales, mark the class-intervals on x-axis and frequencies on y-axis. Note that the scales chosen for both the axes need not be the same.

Step 3. Construct rectangles with class-intervals as bases and the corresponding frequencies as heights.

(B) Frequency Polygon

Let \(x_1, x_2, x_3, \ldots, x_n\) be the class marks (i.e. mid-points) of the given frequency distribution and let \(f_1, f_2, f_3, \ldots, f_n\) be the corresponding frequencies. We plot the points \((x_1, f_1), (x_2, f_2), (x_3, f_3) \ldots, (x_n, f_n)\) on a graph paper and join these points by line segments. We complete the diagram in the form of a polygon by taking two more classes (called imagined classes), one at the beginning and the other at the end.

This polygon is known as the frequency polygon of the given frequency distribution.

Method of Drawing A Frequency Polygon

Steps:

(i) Calculate the class marks \(x_1, x_2, x_3, \ldots, x_n\) of the given class intervals.

(ii) Mark \(x_1, x_2, x_3, \ldots, x_n\) along the x-axis on some suitable scale.

(iii) Mark the frequencies \(f_1, f_2, f_3, \ldots, f_n\) along the y-axis on some suitable scale.

(iv) Join the points \((x_1, f_2), (x_2, f_2), (x_3, f_3), \ldots, (x_n, f_n)\) by line segments.

(v) Take two class intervals each of frequency zero, one at the beginning and the other at the end of the frequency table, find their class marks. (These classes are imagined classes.)

(vi) Join the mid-point of the first class interval to the mid-point of the imagined class at the beginning. Also join the mid-point of the last class interval to the mid-point of the imagined class at the end.

(C) Cumulative Frequency Curve or Ogive

In order to represent a frequency distribution by an ogive, we mark the upper-class limits along x-axis and the corresponding cumulative frequencies along y-axis and join these points by a free hand curve, called an ogive. To complete the ogive, we plot the lower limit of first class interval on x-axis and join this point with first point of the curve.

Method of Drawing an Ogive

Step 1. If the given frequency distribution is in inclusive form, then convert it to an exclusive form.

Step 2. Prepare the cumulative frequency table.

Step 3. Mark the upper-limits of class-intervals along x-axis and their corresponding cumulative frequencies along y-axis.

Step 4. Also, plot the lower-limit of first class-interval with cumulative frequency 0.

Step 5. Join these points by a free hand curve to obtain the required ogive.

Exercise 27

Q.1. Draw a histogram to represent the following data:

Sol. We take marks obtained on x-axis and no. of students on y-axis. Histogram of the given data is given below:

[Histogram image with marks obtained on x-axis (0 to 60) and no. of students on y-axis (0 to 24), showing bars for each class interval]

Q.2. Draw a histogram to represent the following data: (2005)

Sol.

Histogram is given along side:

[Histogram image with pocket money in Rs. on x-axis (150 to 400) and no. of students on y-axis (0 to 12), showing bars for each class interval]

Q.3. Construct a histogram for the following frequency distribution:

Sol. We write the given class intervals in exclusive form and then we will draw the histogram given below:

Data in exclusive form

[Histogram image with class intervals on x-axis (4.5 to 52.5) and frequency on y-axis (0 to 28), showing bars for each class interval]

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