Advertisements
Advertisements
Question
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.
Advertisements
Solution
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:
APPEARS IN
RELATED QUESTIONS
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?
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.
The bar graph shown in Fig 23.16 represents the circulation of newspapers in 10 languages. Study the bar graph and answer the following questions:
(i) What is the total number of newspapers published in Hindi, English, Urdu, Punjabi and Bengali?
(ii) What percent is the number of news papers published in Hindi of the total number of newspapers?
(iii) Find the excess of the number of newspapers published in English over those published in Urdu.
(iv) Name two pairs of languages which publish the same number of newspapers.
(v) State the language in which the smallest number of newspapers are published.
(vi) State the language in which the largest number of newspapers are published.
(vii) State the language in which the number of newspapers published is between 2500 and 3500.
(viii) State whether true or false:
a. The number of newspapers published in Malayalam and Marathi together is less than those published in English.
b. The number of newspapers published in Telugu is more than those published in Tamil.
Read the bar graph given in Fig. 23.17 and answer the following questions:
(i) What information is given by the bar graph?
(ii) What was the crop-production of rice in 1970 - 71?
(iii) What is the difference between the maximum and minimum production of rice?
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 investment (in ten crores of rupees) of Life Insurance Corporation of India in different sectors are given below:
| Sectors | Investment (in ten crores of rupees) |
| Central Government Securities State Government Securities Securities guaranteed by the Government Private Sectors Socially oriented sectors (Plans) Socially oriented sectors (Non-Plan) |
45 11 23 18 46 11 |
Represent the above data with the help of bar graph.
In a histogram the class intervals or the group are taken along
For the following table, draw a bar-graph
| A | B | C | D | E | F |
| 230 | 400 | 350 | 200 | 380 | 160 |
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?
Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement.
