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प्रश्न
The monthly profits (in Rs.) of 100 shops are distributed as follows:
| Profits per shop: | 0-50 | 50-100 | 100-50 | 150-200 | 200-250 | 250-300 |
| No. shops: | 12 | 18 | 27 | 20 | 17 | 6 |
Draw a histogram for the data and show the frequency polygon for it.
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उत्तर
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the horizontal and vertical axes represent the class-intyervals and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with class-intervals as bases and respective frequencies as heights. The scale for horizontal axis may not be same as the scale for vertical axis. Let us take one vertical division is equal to 3 shops.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 0-50 is ` 12/3 = 4` big divisions.
2. The height of the rectangle corresponding to the class-interval 50-100 is `18/3 = 6` big divisions.
3. The height of the rectangle corresponding to the class-interval 100-150 is `27/3 = 9` big divisions.
4. The height of the rectangle corresponding to the class-interval 150-200 is ` 20/3 = 6.67` big divisions.
5. The height of the rectangle corresponding to the class-interval 200-250 is `17/3 = 5.67` big divisions.
6. The height of the rectangle corresponding to the class-interval 250-300 is `6/3 =2` big divisions.
The histogram of the given data is as follows:
For frquency polygon, first we will obtain the class marks as given in the following table.
| Profits per shop | Class Marks | Number of shops |
| 0-50 | 25 | 12 |
| 50-100 | 75 | 18 |
| 100-150 | 125 | 27 |
| 150-200 | 175 | 20 |
| 200-250 | 225 | 17 |
| 250-300 | 275 | 6 |
We plot the points (25, 12), (75, 18), (125, 27), (175, 20), (225, 17) and (275, 6).
Now, we join the plotted points by line segments . The end points (25, 12) and (275, 6) are joined to the mid-points (−25, 0) and (325, 0) respectively of imagined class-intervals to obtain the frequency polygon.
The frequency polygon of the given data is as follows:
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संबंधित प्रश्न
Given below are the seats won by different political parties in the polling outcome of a state assembly elections:-
| Political Party | A | B | C | D | E | F |
| Seats Won | 75 | 55 | 37 | 29 | 10 | 37 |
- Draw a bar graph to represent the polling results.
- Which political party won the maximum number of seats?
Read the bar graph given in Fig. below and answer the following questions:
(i) What information does it give?
(ii) In which part the expenditure on education is maximum in 1980?
(iii) In which part the expenditure has gone up from 1980 to 1990?
(iv) In which part the gap between 1980 and 1990 is maximum?
The following tables gives the quantity of goods (in crore tonnes)
| Year | 1950-51 | 1960-61 | 1965-66 | 1970-71 | 1980-81 | 1982-83 |
| Quantity of Goods (in crore tonnes) |
9 | 16 | 20 | 20 | 22 | 26 |
Explain through the bar graph if the quantity of goods carried by the Indian Railways in 1965-66 is more than double the quantity of goods carried in the year 1950-51.
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 frequency distribution, ogives are graphical representation of
The daily wages in a factory are distributed as follows:
|
Daily wages (in Rs.) |
125 - 175 |
175 - 225 |
225 - 275 |
275 - 325 |
325 - 375 |
|
Number of workers |
4 |
20 |
22 |
10 |
6 |
Draw a frequency polygon for this distribution.
Mr. Kapoor compares the prices (in Rs.) of different items at two different shops A and B. Examine the following table carefully and represent the data by a double bar graph.
| Items | Price (in ₹) at the shop A | Price (in ₹) at the shop B |
|
Tea-set |
900 | 950 |
|
Mixie |
700 | 800 |
|
Coffee-maker |
600 | 700 |
|
Dinner set |
600 | 500 |
The following table shows the market position of different brands of tea-leaves.
| Brand | A | B | C | D | others |
| % of Buyers | 35 | 20 | 20 | 15 | 10 |
Draw it-pie-chart to represent the above information.
The frequency distribution has been represented graphically as follows:
| Marks | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 100 |
| Number of Students | 10 | 15 | 20 | 25 |
Do you think this representation is correct? Why?
Draw a histogram of the following distribution:
| Heights (in cm) | Number of students |
| 150 – 153 | 7 |
| 153 – 156 | 8 |
| 156 – 159 | 14 |
| 159 – 162 | 10 |
| 162 – 165 | 6 |
| 165 – 168 | 5 |
