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प्रश्न
The marks obtained (out of 100) by a class of 80 students are given below:
| Marks | Number of students |
| 10 – 20 | 6 |
| 20 – 30 | 17 |
| 30 – 50 | 15 |
| 50 – 70 | 16 |
| 70 – 100 | 26 |
Construct a histogram to represent the data above.
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उत्तर
See the given table, the class intervals are of unequal width.
So, we calculate the adjusted frequency for each class.
Now, minimum size = 20 – 10 = 10
The formula of adjusted frequencies are:
Adjusted frequency = `("Minimum class" - "size")/("Class" - "size") xx` Frequency of the class
Now, the modified table for frequency distribution is given by:
| Marks | Numbers of students (Frequency) |
Adjusted frequency |
| 10 – 20 | 6 | `10/10 xx 6 = 6` |
| 20 – 30 | 17 | `10/10 xx 17 = 17` |
| 30 – 50 | 15 | `10/20 xx 15 = 15/2 = 7.5` |
| 50 – 70 | 16 | `10/20 xx 16 = 16/2 = 8` |
| 70 – 100 | 26 | `10/30 xx 26 = 26/3 = 8.67` |
Now, let’s construct rectangles with class limits as base and respective adjusted frequencies as height
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संबंधित प्रश्न
The following table gives the distribution of students of two sections according to the mark obtained by them:-
| Section A | Section B | ||
| Marks | Frequency | Marks | Frequency |
| 0 - 10 | 3 | 0 - 10 | 5 |
| 10 - 20 | 9 | 10 - 20 | 19 |
| 20 - 30 | 17 | 20 - 30 | 15 |
| 30 - 40 | 12 | 30 - 40 | 10 |
| 40 - 50 | 9 | 40 - 50 | 1 |
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
Study the bar graph representing the number of persons in various age groups in a town shown in Fig. below. Observe the bar graph and answer the following questions:
(i) What is the percentage of the youngest age-group persons over those in the oldest age group?
(ii) What is the total population of the town?
(iii) What is the number of persons in the age group 60 - 65?
(iv) How many persons are more in the age-group 10 - 15 than in the age group 30 - 35?
(v) What is the age-group of exactly 1200 persons living in the town?
(vi) What is the total number of persons living in the town in the age-group 50 - 55?
(vii) What is the total number of persons living in the town in the age-groups 10 - 15 and 60 - 65?
(viii) Whether the population in general increases, decreases or remains constant with the increase in the age-group.
Read the bar graph given in Fig. 23.19 and answer the following questions:
(i) What information is given by the bar graph?
(ii) In which years the areas under the sugarcane crop were the maximum and the minimum?
(iii) State whether true or false:
The area under the sugarcane crop in the year 1982 - 83 is three times that of the year 1950 - 51
Read the bar graph given in Fig. 23.21 and answer the following questions:
(i) What is the information given by the bar graph?
(ii) What is the number of families having 6 members?
(iii) How many members per family are there in the maximum number of families? Also tell the number of such families.
(iv) What are the number of members per family for which the number of families are equal? Also, tell the number of such families?
The following data gives the demand estimates of the Government of India, Department of Electronics for the personnel in the Computer sector during the Eighth Plan period (1990-95):
| Qualifications: | MCA (Master in Computer applications) |
DCA (Diploma in Computer Applications) |
DCE (Diploma in Computer Engineering) |
CL (Certificate Level Course) |
ST (Short-term Course) |
| Personnel Required | 40600 | 181600 | 18600 | 670600 | 1802900 |
Represent the data with the help of a bar graph. Indicate with the help of the bar graph the course where estimated requirement is least.
Construct a histogram for the following data:
| Monthly School fee (in Rs): |
30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 | 210-240 |
| No of Schools | 5 | 12 | 14 | 18 | 10 | 9 | 4 |
The following tables show the mode of transport used by boys and girls for going to the same school.
| Bus | Bicycle | Walking | Other sources | |
|
Number of boys |
80 | 60 | 20 | 85 |
|
Number of girls |
90 | 75 | 35 | 60 |
Draw a double bar graph representing the above data.
Mr. Mirza’s monthly income is Rs. 7,200. He spends Rs. 1,800 on rent, Rs. 2,700 on food, Rs. 900 on the education of his children; Rs. 1,200 on Other things and saves the rest.
Draw a pie-chart to represent it.
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 |
Draw a histogram to represent the following grouped frequency distribution:
| Ages (in years) | Number of teachers |
| 20 – 24 | 10 |
| 25 – 29 | 28 |
| 30 – 34 | 32 |
| 35 – 39 | 48 |
| 40 – 44 | 50 |
| 45 – 49 | 35 |
| 50 – 54 | 12 |
