**26. Bar diagram is a:****(a) one-dimensional diagram****(b) two-dimensional diagram****(c) diagram with no dimension****(d) none of these**

**Ans.** (a) one-dimensional diagr

**Explanation:**

Bar diagram is a one-dimensional diagram as these are presented on a plane having two axis in form of rectangular bars. The width is of no concern and only the length shows the frequency of the class interval.

**27. Data represented through a histogram can help in finding graphically the:****(a) mean****(b) mode****(c) median****(d) all of these**

**Ans.** (b) mode

**Explanation:**

Histogram gives the value of mode of the frequency distribution presented graphically with the help of the tallest rectangle.

**28. Ogives can be helpful in locating graphically the:****(a) mode****(b) mean****(c) median****(d) none of these**

**Ans.** (c) median

**Explanation:**

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

**29. Data represented through arithmetic line graph help in understanding:****(a) long term trend****(b) cyclicity in data****(c) seasonality in data****(d) all of the above**

**Ans.** (a) long term trend

**Explanation:**

Arithmetic line graph assists in knowing the periodicity, trend, etc. in a long term time series data.

**30. Width of bars in a bar diagram need not be equal. (True/False)**

**Ans.** False. Bar diagram consist of a group of equiwidth and equispaced rectangular bars for each set of data.

**31. Width of rectangles in a histogram should essentially be equal. (True/False) **

**Ans. **False. When the class intervals are of same width, then the rectangular area are proportional to their corresponding frequencies and width of rectangles are equal. But, sometimes it is useful or required to use different width of class intervals and hence width of rectangles are unequal.

**32. Histogram can only be formed with continuous classification of data. (True/False)**

**Ans.** True. A histogram is useful for showing only continous data and not for discrete series or data. If the classes are not continuous in nature, then one have to first convert it into continuous intervals.

**33. Histogram and column diagram are the same method of presentation of data. (True/False)**

**Ans.** False. Histogram is a two-dimensional diagram which is useful for showing continuous data and the rectangles do not have the spaces between them, whereas column diagram is one-dimensional diagram having spaces between every bar or rectangle.

**34. Mode of a frequency distribution can be known graphically with the help of histogram. (True/False)**

**Ans.** True. Histogram gives the value of mode of the frequency distribution presented graphically and gives the value through the tallest rectangle.

**35. Median of a frequency distribution cannot be known from the ogives. (True/False) **

**Ans. **False. Intersection point of the more than and less than ogives gives the value of median.

**36. What kind of diagrams are more effective in representing the following? (a) Monthly rainfall in a year (b) Composition of the population of Delhi by religion (c) Components of cost in a factory**

**Ans.** (a) The monthly rainfall in a year can be easily represented by using a bar diagram because of only one variable, i.e., monthly rainfall. The months are plotted on x-axis and rainfall on Y-axis.

(b) Composition of the population of Delhi by religion is best represented by using a component bar diagram. It displays the bar and its sub-divisions into two or more components. Therefore, the total population can be sub divided on the basis of religion and presented using a component bar diagram.

(c) Components of the cost in a factory can easily be represented using a pie chart. The circle signifies the total cost and several components of the costs are presented by different portions of the circle drawn as per the percentage of total cost.

**37. Suppose you want to emphasise the increase in the share of urban non-workers and lower level of urbanisation in India as shown in Example 4.2. How would you do it in the tabular form?**

**Ans.** Share of urban workers and non-workers in India

Location | |||

Sex | Worker in urban (in crore) | Non-worker in urban (in crore) | Total |

Male | 50 | 70 | 120 |

Female | 25 | 50 | 75 |

Total | 75 | 120 | 195 |

**38. How does the procedure of drawing a histogram differ when class intervals are unequal in comparison to equal class intervals in a frequency table?**

**Ans.** A histogram is a set of rectangles having bases as the intervals between class boundaries shown on X-axis and having areas proportional to the class frequency shown on y-axis. In case, the class intervals are of equal width, the rectangular area are proportional to their corresponding frequencies.

Though, sometimes it is useful or at times it is required, to use different width of class intervals. So, in this case, the height for rectangualr area is the quotient of height, that is, frequency and base, that is, width of the class interval. But if we have equal intervals, then all the rectangles will have the same base and area can be easily represented by the frequency.

How ever, if the bases vary in their width, then the heights of rectangles need to be adjusted by dividing class frequency by class interval’s width in place of absolute frequency. This gives us the frequency density. Thus, Frequency density = Width of the class frequency of the class interval.

**39. The Indian Sugar Mills Association reported that, ‘sugar production during the first fortnight of December 2001 was about 3,87,000 tonnes, as against 3,78,000 tonnes during the same fortnight last year (2000). The off take of sugar from factories during the first fortnight of December 2001 was 2,83,000 tonnes for internal consumption and 41,000 tonnes for exports as against 1,54,000 tonnes for internal consumption and nil for exports during the same fortnight last season.’****(i) Present the data in tabular form.****(ii) Suppose you were to present these data in diagrammatic form which of the diagrams would you use and why?****(iii) Present these data diagrammatically.**

**Ans.** (i) Sugar Production in India

Total Production (tonnes) | Off-take for Internal Consumption (tonnes) | Off-take for Exports (tonnes) | |

December 2000 | 378000 | 154000 | — |

December 2001 | 387000 | 283000 | 41000 |

(ii) This data can be effectively presented in diagrammatic form using the multiple bar diagram because multiple bar diagrams are used for comparison of two or more sets of data for different classes, years, etc.

**40. The following table shows the estimated sectoral real growth rates (percentage change over the previous year) in GDP at factor cost.**

Year (1) | Agriculture and allied sectors (2) | Industry (3) | Services (4) |

1994 – 95 | 5.0 | 9.2 | 7.0 |

1995 – 96 | – 0.9 | 11.8 | 10.3 |

1996 – 97 | 9.6 | 6.0 | 7.1 |

1997 – 98 | – 1.9 | 5.9 | 9.0 |

1998 – 99 | 7.2 | 4.0 | 8.3 |

1999 – 2000 | 0.8 | 6.9 | 8.2 |

**Represent the data as multiple time-series graphs.**