MATHS 4 Marks Questions

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let u consider that the vertical and horizontal axes represent the refineries and the production of oil in la] tonnes respectively. We have to draw 5 bars of different lengths given in the table. At first, we mark 5 points in the vertical axis at equal distances and erect rectangles of the same wk at these points. The lengths of the rectangles are proportional to the productions of oil.The horizontal bar graph of the given data is following:

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the income or expenditure in thousand rupees respectively. We have to draw 5 bars for each income and expenditure side by side of different lengths given in the table.
At first, we mark 5 points for each income and expenditure in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the corresponding income or expenditures.

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the interests in lakhs of rupees respectively. We have to draw 5 bars of different lengths given in the table. At first, we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the interests paid by the company.The vertical bar graph of the given data is following:

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the route lengths in thousand km respectively. We have to draw 5 bars of different lengths given in the table. At first we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the route lengths.The vertical bar graph of the given data is following:

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the number of applicants registered in thousands respectively. We have to draw 6 bars of different lengths given in the table. At first we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the number of applicants registered.The vertical bar graph of the given data is following:

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the amount of loan in Crores of rupees respectively. We have to draw 5 bars of different lengths given in the table. At first, we mark 5 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the amount of loan disbursed by the bank.

1. The vertical bar graph of the given data is following:

2. It is seen from the bar graph that the heights of the bars in the years 1994 and 1995 are same. Hence, the amount of loan is not increased in the year 1995 over the preceding year 1994.

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the years and the production of food grains in thousand tonnes respectively. We have to draw 6 bars of different lengths given in the table. At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the production of food grains. The vertical bar graph of the given data is following:

To represent the given data by a vertical bar graph, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the countries and the average age of men’s respectively. We have to draw 6 bars of different lengths given in the table. At first, we mark 6 points in the horizontal axis at equal distances and erect rectangles of the same width at these points. The heights of the rectangles are proportional to the average age of men’s in different countries.The vertical bar graph of the given data is following:

The given information can be represented using a pictograph in the following manner:

We first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. To draw the frequency polygon of the given data without using histogram, obtain the class-limits of the class intervals. Obtain the class-limits of two class-intervals of 0 frequencies, i.e. on the horizontal axis, one adjacent to the first, on its left and one adjacent to the last, on its right. These class-intervals are known as imagined class-intervals. Then plot the frequencies against class-limits.
The following table is useful to draw the frequency polygon of the given data.

Class-Intervals	Class-Marks	Frequency
55.5-62.5	59	0
62.5-69.5	66	1
69.5-76.5	73	3
76.5-83.5	80	5
83.5-90.5	87	15
90.5-97.5	94	12
97.5-104.5	101	10
104.5-111.5	108	6
111.5-118.5	115	4
118.5-125.5	122	3
125.5-132.5	129	1
132.5-139.5	136	0

We represent class marks on X-axis on a suitable scale and the frequencies on Y-axis on a suitable scale.
To obtain the frequency polygon we plot the points (66, 1), (73, 3), (80, 5), (87, 15), (94, 12), (101, 10), (108, 6), (115, 4), (122, 3), (129, 1).
Now we join the plotted points by line segments. The end points (66, 1) and (129, 1) are joined to the mid points (59, 0) and (136, 0) respectively of imagined class intervals to obtain the frequency polygon.

A bar graph is a diagram consisting of a sequence of vertical or horizontal bars or rectangles, each of which represents an equal interval of the values of a variable, and has the height proportional to the quantities of the phenomenon under consideration in that interval. A bar graph may also be used to illustrate discrete data, in which case each bar represents a distinct circumstance.
While drawing a bar graph, we keep in mind that:

• The width of the bars should be uniform throughout.
• The gap between any two bars should be uniform throughout.
• Bars may be either horizontal or vertical.

Each bar must be of the same width and the gap between them must be uniform. Make sure that the width of the bars and the gap between them should not be necessarily same.

1. The bar graph represents the import and export (in 100 Crores of rupees) from 1982–83 to 1986–87.
2. The export is minimum in the year 1982-83 at the height of the bar corresponding to export is minimum in the year 1982–83.
3. The import is maximum in the year 1986-87 as the height of the bar corresponding to import is maximum in the year 1986–87.
4. The bars of export and import are side by side. Clearly, it is seen from the bar graph that the difference between the values of export and import is maximum in the year 1986–87.

It is seen from the bar graph that the height of the 3s bar from the left is least, which is corresponding to DCE. Hence, the requirement is least in DCE.

1. The bar graph represents the number of tickets of different state lotteries sold by an agent on a day.
2. The number of tickets of Assam State Lottery were sold by the agent is 40.
3. The maximum numbers of tickets were sold is 100, in the state Haryana
4. The maximum number of tickets were sold is 100, in the state Haryana the minimum number of tickets were sold is 20, in the state Rajasthan. It is clear that 100 are equal to the 5 times of 20. Hence, the statement is false.
5. The minimum numbers of tickets were sold is 20, in the state Rajasthan.

1.  

Time taken to solve a problem	Number of pupils
10-20	1
20-30	5
30-40	4
40-50	8
50-60	5
60-70	2

 

2.  

1. The bar graph represents the public expenditure on education in different countries and sub continents in the years 1980 and 1990.
2. The expenditure on education in Africa in 1980 is the maximum.
3. It is clear from the bar graph that in East Africa the expenditure has gone up from 1980 to 1990.
4. It is observed from the bar graph that the gap between expenditures in 1980 and 1990 is maximum in Africa, which is 18 - 14 = 4%