NCERT Solution for Class 11 Statistics Chapter 4: Presentation of Data

(c) Intersection point of the less than and more than ogives gives the median.

False
Bar diagram comprises a group of equispaced and equi width rectangular bars for each class or category of data.

False
Intersection-point of the less than and more than ogives gives the median.

(a) Bar diagrams are one-dimensional diagrams. Though these are represented on a plane of two axes in the form of rectangular bars, the width is of no consequence and only the length depicts the frequency.

(b) Histogram gives the value of mode of the frequency distribution graphically through the highest rectangle.

(a) Arithmetic line graph helps in understanding the trend, periodicity, etc in a long term time series data.

False
If the class intervals are of equal width, the area of the rectangles are proportional to their respective frequencies and width of rectangles will be equal. However, sometimes it is convenient or necessary to use varying width of class intervals and hence unequal width of rectangles.

True
A histogram is never drawn for a discrete variable/data. If the classes are not continuous they are first converted into continuous classes.

False
Histogram is a two dimensional diagram drawn for continuous data and the rectangles do not have spaces in between while column diagram is one dimensional with space in between every column (bar).

True
Histogram gives value of mode of the frequency distribution graphically through the highest rectangle.

(a) The monthly rainfall in a year can be best represented by a bar diagram as only one variable i.e., monthly rainfall is to be presented diagrammatically. The rainfall is plotted on Y-axis in the corresponding month that is plotted on the X-axis.
(b) Composition of the population of Delhi by religion can be represented by a component bar diagram. A component bar diagram shows the bar and its sub-divisions into two or more components. Thus, the total population can be subdivided in terms of religion and presented through a component bar diagram.
(c) Different components of cost in a factory can most effectively be depicted through a pie chart. The circle represents the total cost and various components of costs are shown by different portions of the circle drawn according to the percentage of total cost each component covers.

Share of urban workers and non workers in India

A histogram is a set of rectangles with bases as the intervals between class boundaries (along X-axis) and with areas proportional to the class frequency. If the class intervals are of equal width, the area of the rectangles are proportional to their respective frequencies.

However, sometimes it is convenient or at times necessary, to use varying width of class intervals. For graphical representation of such data, height for area of a rectangle is the quotient of height i.e., frequency and base i.e., width of the class interval. When intervals are equal, all rectangles have the same base and area can conveniently be represented by the frequency of the interval.

But, when bases vary in their width, the heights of rectangles are to be adjusted to yield comparable measurements by dividing class frequency by width of the class interval instead of absolute frequency. This gives us the frequency density for the purpose of comparison.
Thus 

 Frequency density 

( Height of rectangle )

=

 Class Frequency 

 Width of the class interval 

(i) Data in tabular form.
Sugar Production in India

(ii) The data can effectively be presented diagrammatically using the multiple bar diagram. This is because multiple bar diagrams are used for comparing two or more sets of data for different years or classes, etc.