Q.16. List the different kinds of diagrams.
Ans. The different kinds of diagrams are:
(i) Geometric diagrams – bar diagram and pie diagram
(ii) Frequently diagrams – histogram, frequency polygon, frequency curve and ogive
(iii) Arithmetic line diagram or time-series graph
Q.17. How are data presented in bar diagram?
Ans. In bar diagrams, data are presented in the form of bars or rectangles.
Q.18. List the variables which can be best represented by bar diagram?
Ans. Discrete variables such as family size, grades in an exam, etc. and attributes such as gender, religion, caste, etc. can be best represented by bar diagram.
Q.19. State the use of multiple bar diagram.
Ans. Multiple bar diagrams are used to show two or more sets of data simultaneously.
Q.20. What is a component bar diagram?
Ans. A component bar diagram represents the bar and its sub-divisions into two or more components.
Q.21. Why is there no open space between two consecutive rectangles of a histogram?
Ans. While preparing a histogram, the lower class boundary of a class interval coincides with the upper class boundary of the previous interval. Thus, all the rectangles are adjacent and there is no open space between two consecutive rectangles.
Q.22. Define frequency polygon.
Ans. Frequency polygon is a plane connected by line segments, formed by joining the middle-top points of all rectangles in a histogram.
Q.23. What type of distribution is represented by an ogive?
Ans. An ogive represents cumulative frequency distribution.
Q.24. How is arithmetic line graph prepared?
Ans. Time is plotted along x-axis and the value of the variable along y-axis. The plotted points are joined to obtain arithmetic line graph.
Q.25. State the rules for constructing diagrams.
Ans. Following are the rules for constructing diagrams:
(i) The diagram should be drawn strictly according to the scale.
(ii) Title of diagram should not only be easy, definite and attractive but also self-explanatory.
(iii) Necessary instructions and colours should be used along with their clarification.
(iv) The use of words and numbers should be minimum.
(v) Diagram should be neatly bordered with thick and double lines.
(vi) Diagram should always be easy and understandable.
(vii) Diagram formation should always be from left to right and up to down.
(viii) Basis of data should be clearly mentioned.
Q.26. Write the features of bar diagrams.
Ans. The main features of bar diagrams are:
(i) Height of bar diagram changes with the change in the frequency.
(ii) Width of all the bars is same.
(iii) Bars can be drawn either vertically or horizontally.
(iv) The distance between the bars should be equal.
Q.27. Explain the various types of bar diagrams.
Ans. The various types of bar diagrams are explained below:
(i) Simple Bar Diagram: In simple bar diagrams, data are presented through equi-width and equidistant bars or rectangles. Bars of different heights are made corresponding to a particular characteristic, say population, production, literacy, etc. at various points of time or of different states to construct a simple bar diagram.
(ii) Multiple Bar Diagram: Multiple bar diagrams are used to show two or more sets of data simultaneously. For example, sales and profits, exports and imports, production of vegetables and foodgrains can be shown using multiple bar diagrams.
(iii) Component Bar Diagram: A component bar diagram represents the bar and its sub-divisions into two or more components. It is very useful in comparing the sizes of different components. For example, distribution of population into males, females and children; expenditure pattern in a typical Indian family; etc.
Q.28. What are the different types of component bar diagrams.
Ans. There are two types of component bar diagrams:
(i) Simple Component Bar Diagram: It helps in comparing the size of various elements or components and also shows relationship between the integral parts. These are represented in absolute values. Comparative bars are differentiated with colours or shades.
(ii) Percentage Component Bar Diagram: The area of the bar is proportionally divided among various sets of data or components. It is used when the values have high magnitude. The value of total bar length is considered as 100 and value of all the items is calculated as percentage and presented in the form of diagram.
Q.29. Write the steps to determine mode graphically.
Ans. The steps to determine mode graphically are given below:
(i) Represent the given data in the form of a histogram. The height of the rectangles in the histogram shows the frequencies of the class interval.
(ii) Identify the highest rectangle. The class interval corresponding to the highest rectangle is the modal class of the series.
(iii) Join the top left corner of the modal rectangle with top right corner of the rectangle on the right. Also, join the top right corner of the modal rectangle with top left corner of the rectangle on the left.
(iv) Draw a perpendicular line from the point of intersection onto the x-axis.
(v) The value at which the perpendicular meets the x-axis will give the mode.
Q.30. State the difference between:
(i) ‘Less than’ and ‘more than’ ogive
(ii) Frequency polygon and frequency curve
Ans. (i) In ‘less than’ ogive, frequencies less than the upper class limit are shown. On the other hand, in ‘more than’ ogive, frequencies greater than the lower class limit are shown.
(ii) Frequency polygon is a plane connected by line segments, formed by joining the middletop points of all rectangles in a histogram. On the other hand, frequency curve is a smooth freehand curve, which passes very closely through the points of the frequency polygon.