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प्रश्न
Construct a frequency polygon for the following data:
| Class-Intervals | 10-14 | 15-19 | 20-24 | 25-29 | 30-34 |
| Frequency | 5 | 8 | 12 | 9 | 4 |
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उत्तर
The class intervals are inclusive. We will first convert them into the exclusive form.
| Class-Interval | Frequency |
| 9.5-14.5 | 5 |
| 14.5-19.5 | 8 |
| 19.5-24.5 | 12 |
| 24.5-29.5 | 9 |
| 29.5-34.5 | 4 |
Steps:
- Draw a histogram for the given data.
- Mark the mid-point at the top of each rectangle of the histogram drawn.
- Also, mark the mid-point of the immediately lower class-interval and the mid-point of the immediately higher class-interval.
- Join the consecutive mid-points marked by straight lines to obtain the required frequency polygon.
The required frequency polygon is as follows:
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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?
A random survey of the number of children of various age groups playing in a park was found as follows:
| Age (in years) | Number of children |
| 1 - 2 | 5 |
| 2 - 3 | 3 |
| 3 - 5 | 6 |
| 5 - 7 | 12 |
| 7 - 10 | 9 |
| 10 - 15 | 10 |
| 15 - 17 | 4 |
Draw a histogram to represent the data above.
The following bar graph (Fig. 23. 1 4) represents the heights (in cm) of 50 students of Class XI of a particular school. Study the graph and answer the following questions:
(i) What percentage of the total number of students have their heights more than 149cm?
(ii) How many students in the class are in the range of maximum height of the class?
(iii) The school wants to provide a particular type of tonic to each student below the height
of 150 cm to improve his height. If the cost of the tonic for each student comes out to be Rs. 55, how much amount of money is required?
(iv) How many students are in the range of shortest height of the class?
(v) State whether true or false:
a. There are 9 students in the class whose heights are in the range of 155 - 159 cm.
b. Maximum height (in cm) of a student in the class is 17.
c. There are 29 students in the class whose heights are in the range of 145- 154 cm.
d. Minimum height (in cm) of a student is the class is in the range of 140 – 144 cms.
e. The number of students in the class having their heights less than 150 cm is 12.
f. There are 14 students each of whom has height more than 154. cm.
The population of Delhi State in different census years is as given below:
| Census year | 1961 | 1971 | 1981 | 1991 | 2001 |
| Population in Lakhs | 30 | 55 | 70 | 110 | 150 |
The following data gives the amount of loans (in crores of rupees) disbursed by a bank during some years:
| Year | 1992 | 1993 | 1994 | 1995 | 1996 |
| Loan (in crores of rupees) |
28 | 33 | 55 | 55 | 80 |
(i) Represent the above data with the help of a bar graph.
(ii) With the help of the bar graph, indicate the year in which amount of loan is not increased over that of the preceding year.
The production of oil (in lakh tonnes) in some of the refineries in India during 1982 was given below:
| Refinery: | Barauni | Koyali | Mathura | Mumbai | Florida |
| Production of oil (in lakh tonnes) |
30 | 70 | 40 | 45 | 25 |
Construct a bar graph to represent the above data so that the bars are drawn horizontally.
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.
Draw a histogram for the daily earnings of 30 drug stores in the following table:
| Daily earning (in Rs): |
450-500 | 500-550 | 550-600 | 600-650 | 650-700 |
| Number of Stores: | 16 | 10 | 7 | 3 | 1 |
Which one of the following is not the graphical representation of statistical data:
The percentage of marks obtained, in different subjects by Ashok Sharma (in an examination) is given below. Draw a bar graph to represent it.
| English | Hindi | Maths | Science | Social Studies |
| 85 | 60 | 35 | 50 | 70 |
