Advertisements
Advertisements
प्रश्न
Draw, in the same diagram, a histogram and a frequency polygon to represent the following data which shows the monthly cost of living index of a city in a period of 2 years:
| Cost of living index: |
440-460 | 460-480 | 480-500 | 500-520 | 520-540 | 540-560 | 560-580 | 580-600 |
| No. of months: | 2 | 4 | 3 | 5 | 3 | 2 | 1 | 4 |
Advertisements
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-limits 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. It should be noted that the scale for horizontal axis may not be same as the scale for vertical axis. To draw the frequency polygon of the given data using histogram, obtain the mid-points of the upper horizontal side of each rectangle and then join these mid-points of the adjacent rectangles of the histogram by line segments. Obtain the mid-points 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. Complete the polygon by joining the mid-points of first and last class-intervals to the mid-points of imagined class-intervals adjacent to them. Let us take one vertical division is equal to 1 month.
The heights of the different rectangles are as follows:
1. The height of the rectangle corresponding to the class-interval 440-460 is 2 big divisions.
2. The height of the rectangle corresponding to the class-interval 460-480 is 4 big divisions.
3. The height of the rectangle corresponding to the class-interval 480-500 is 3 big divisions.
4. The height of the rectangle corresponding to the class-interval 500-520 is 5 big divisions.
5. The height of the rectangle corresponding to the class-interval 520-540 is 3 big divisions.
6. The height of the rectangle corresponding to the class-interval 540-560 is 2 big divisions.
7. The height of the rectangle corresponding to the class-interval 560-580is 1 big division.
8. The height of the rectangle corresponding to the class-interval 580-600 is 4 big divisions.
The histogram and frequency polygon of the given data is as follows:
APPEARS IN
संबंधित प्रश्न
The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:-
| Length (in mm) | Number of leaves |
| 118 - 126 | 3 |
| 127 - 135 | 5 |
| 136 - 144 | 9 |
| 145 - 153 | 12 |
| 154 - 162 | 5 |
| 163 - 171 | 4 |
| 172 - 180 | 2 |
- Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
- Is there any other suitable graphical representation for the same data?
- Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?
The following table gives the life times of 400 neon lamps:-
| Life time (in hours) | Number of lamps |
| 300 - 400 | 14 |
| 400 - 500 | 56 |
| 500 - 600 | 60 |
| 600 - 700 | 86 |
| 700 - 800 | 74 |
| 800 - 900 | 62 |
| 900 - 1000 | 48 |
- Represent the given information with the help of a histogram.
- How many lamps have a life time of more than 700 hours?
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. 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?
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?
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 is the distribution of total household expenditure (in Rs.) of manual worker in a city:
| Expenditure (in Rs): |
100-150 | 150-200 | 200-250 | 250-300 | 300-350 | 350-400 | 400-450 | 450-500 |
| No. of manual workers: | 25 | 40 | 33 | 28 | 30 | 22 | 16 | 8 |
Draw a histogram and a frequency polygon representing the above data.
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.
Draw frequency polygons for each of the following frequency distribution:
(a) using histogram
(b) without using histogram
|
C.I |
5 -15 | 15 -25 | 25 -35 | 35 - 45 | 45-55 | 55-65 |
| ƒ | 8 | 16 | 18 | 14 | 8 | 2 |
The number of students (boys and girls) of class IX participating in different activities during their annual day function is given below:
| Activities | Dance | Speech | Singing | Quiz | Drama | Anchoring |
| Boys | 12 | 5 | 4 | 4 | 10 | 2 |
| Girls | 10 | 8 | 6 | 3 | 9 | 1 |
Draw a double bar graph for the above data.
