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
Read the bar graph shown in Fig. 23.8 and answer the following questions:
(i) What is the information given by the bar graph?
(ii) How many tickets of Assam State Lottery were sold by the agent?
(iii) Of which state, were the maximum number of tickets sold?
(iv) State whether true or false.
The maximum number of tickets sold is three times the minimum number of tickets sold.
(v) Of which state were the minimum number of tickets sold?
Given below (Fig. below) is the bar graph indicating the marks obtained out of 50 in mathematics paper by 100 students. Read the bar graph and answer the following questions:
(i) It is decided to distribute work books on mathematics to the students obtaining less than 20 marks, giving one workbook to each of such students. If a work book
costs Rs 5, what sum is required to buy the work books?
(ii) Every student belonging to the highest mark group is entitled to get a prize of Rs. 10. How much amount of money is required for distributing the prize money?
(iii) Every student belonging to the lowest mark—group has to solve 5 problems per day. How many problems, in all, will be solved by the students of this group per day?
(iv) State whether true or false.
a. 17% students have obtained marks ranging from 40 to 49.
b. 59 students have obtained marks ranging from 10 to 29.
(v) What is the number of students getting less than 20 marks?
(vi) What is the number of students getting more than 29 marks?
(vii) What is the number of students getting marks between 9 and 40?
(viii) What is the number of students belonging to the highest mark group?
(ix) What is the number of students obtaining more than 19 marks?
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?
(iv) Which state has total production of rice and wheat as its maximum?
(v) Which state has the total production of wheat and rice minimum?
The following bar graph shows the results of an annual examination in a secondary school. Read the bar graph and choose the correct alternative in each of the following:
(i) The pair of classes in which the results of boys and girls are inversely proportional are:
(a) VI, VIII (b) VI, IX (c) VIII, IX (d) VIII, X
(ii) The class having the lowest failure rate of girls is
(a) VII (b) X (c) IX (d) VIII
(iii)The class having the lowest pass rate of students is
(a) VI (b) VII (c) VIII (d) IX
The following table shows the daily production of T. V. sets in an industry for 7 days of a week:
| Day | Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
| Number of T.V. Sets | 300 | 400 | 150 | 250 | 100 | 350 | 200 |
Represent the above information by a pictograph .
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.
The following data gives the value (in crores of rupees) of the Indian export of cotton textiles for different years:
| Years | 1982 | 1983-1984 | 1984-1985 | 1985-1986 | 1986-1987 |
| Value of Export of Cotton Textiles (in crores of rupees) |
300 | 325 | 475 | 450 | 550 |
Represent the above data with the help of a bar graph. Indicate with the help of a bar graph the year in which the rate of increase in exports is maximum over the preceding year.
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 |
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.
In a diagnostic test in mathematics given to students, the following marks (out of 100) are recorded:
46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44
Which ‘average’ will be a good representative of the above data and why?
