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प्रश्न
Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:
| Class interval (km/h) | Frequency |
| 30 – 40 | 3 |
| 40 – 50 | 6 |
| 50 – 60 | 25 |
| 60 – 70 | 65 |
| 70 – 80 | 50 |
| 80 – 90 | 28 |
| 90 – 100 | 14 |
Draw a histogram and frequency polygon representing the data above.
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उत्तर
Clearly, the given frequency distribution is in exclusive form.
Along the horizontal axis, we represent the class intervals on some suitable scale. The corresponding frequencies are represented along the vertical axis on a suitable scale.
We construct rectangles with class intervals as the bases and the respective frequencies as the heights.
Let us draw a histogram for this data and mark the mid-points of the top of the rectangles as B, C, D, E, F, G and H, respectively. Here, the first class is 30 – 40 and the last class is 90 – 100.
Also, consider the imagined classes 20 – 30 and 100 – 110 each with frequency 0. The class marks of these classes are 25 and 105 at the points A and I, respectively.
Join all these points by dotted line.
Then, the curve ABCDEFGHI is the required frequency polygon.
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संबंधित प्रश्न
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(i) What is the information given by the bar graph?
(ii) What was the number of commercial banks in 1977?
(iii) What is the ratio of the number of commercial banks in 1969 to that in 1980?
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Read the following bar graph and answer the following questions:
(i) What information is given by the bar graph?
(ii) Which state is the largest producer of rice?
(iii) Which state is the largest producer of wheat?
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(v) Which state has the total production of wheat and rice minimum?
Read the bar graph given in Fig. 23.17 and answer the following questions:
(i) What information is given by the bar graph?
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Read the bar graph given in Fig. 23.19 and answer the following questions:
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The area under the sugarcane crop in the year 1982 - 83 is three times that of the year 1950 - 51
The income and expenditure for 5 years of a family is given in the following data:
| Years | 1995-96 | 1996-97 | 1997-98 | 1998-99 | 1999-2000 |
| Income (Rs. inthousands) |
100 | 140 | 150 | 170 | 210 |
| Expenditure (Rs. in thousands) |
80 | 130 | 145 | 160 | 190 |
Represent the above data by a gar graph.
The following table gives the distribution of IQ's (intelligence quotients) of 60 pupils of class V in a school:
| IQ's: | 125.5 to 13.25 |
118.5 to 125.5 |
111.5 to 118.5 |
104.5 to 111.5 |
97.5 to 104.5 |
90.5 to 97.5 |
83.5 to 90.5 |
76.5 to 83.5 |
69.5 to 76.5 |
62.5 to 69.5 |
| No. of pupils: |
1 | 3 | 4 | 6 | 10 | 12 | 15 | 5 | 3 | 1 |
Draw a frequency polygon for the above data.
In a histogram the area of each rectangle is proportional to
Read the following bar graph and answer the following questions:
a. What information is given by the graph?
b. Which state is the largest producer of wheat?
c. Which state is the largest producer of sugar?
d. Which state has total production of wheat and sugar as its maximum?
e. Which state has the total production of wheat and sugar minimum?
The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table:
| Length (in mm) | Number of leaves |
| 118 – 126 | 8 |
| 127 – 135 | 10 |
| 136 – 144 | 12 |
| 145 – 153 | 17 |
| 154 – 162 | 7 |
| 163 – 171 | 5 |
| 172 – 180 | 3 |
Draw a histogram to represent the data above.
Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a high way:
| Class interval (km/h) | Frequency |
| 30 – 40 | 3 |
| 40 – 50 | 6 |
| 50 – 60 | 25 |
| 60 – 70 | 65 |
| 70 – 80 | 50 |
| 80 – 90 | 28 |
| 90 – 100 | 14 |
Draw the frequency polygon representing the above data without drawing the histogram.
