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प्रश्न
The following histogram shows the frequency distribution f the ages of 22 teachers in a school:
(i) What is the number of eldest and youngest teachers in the school?
(ii) Which age group teachers are more in the school and which least?
(iii) What is the size of the classes?
(iv) What are the class marks of the classes?
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उत्तर
(i) The eldest (50-55 years) = 1 person
This is because the height of the rectangle with class interval 50-55 as base is 1 unit.
The youngest (20-25 years)= 2 persons
This is because the height of the rectangle with class interval 20-25 as base is 2 units.
(ii) The group containing the most number of teachers is 35-40 years. This is because the height of the rectangle with class interval 35-40 as base is the maximum.
The group containing the least number of teachers is 50-55 years. This is because the height of the rectangle with class interval 50-55 as base is the minimum.
(iii) Class size = The range between the upper and the lower boundaries of the class
For example, the size of the class 20-25 years is 5.
\[\text{ Class mark }= \frac{\text{ Upper limit }+\text{ Lower limit}{2}\]
For class 20 - 25:
\[\text{ Class mark }= \frac{20 + 25}{2} = \frac{45}{2} = 22 . 5\]
Similarly, the class marks of the other classes are 27.5; 32.5; 37.5; 42.5; 47.5; 52.5.
संबंधित प्रश्न
Draw a histogram for the frequency table made for the data in Question 3 and answer the following questions.
(1) Which group has the maximum number of workers?
(2) How many workers earn Rs 850 and more?
(3) How many workers earn less than Rs 850?
Draw histogram and frequency polygon on the same graph paper for the following frequency distribution
| Class | Frequency |
| 15-20 | 20 |
| 20-25 | 30 |
| 25-30 | 50 |
| 30-35 | 40 |
| 35-40 | 25 |
| 40-45 | 10 |
Observe the following frequency polygon and write the answers of the questions below it.
- Which class has the maximum number of students?
- Write the classes having zero frequency.
- What is the class-mark of the class, having frequency of 50 students?
- Write the lower and upper class limits of the class whose class mark is 85.
- How many students are in the class 80-90?
Draw a histogram of the following data:
| Class interval: | 10−15 | 15−20 | 20−25 | 25−30 | 30−35 | 34−40 |
| Frequency: | 30 | 98 | 80 | 58 | 29 | 50 |
Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:
| Variate | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| Frequency | 1 | 2 | 3 | 1 | 2 | 4 | 2 | 1 | 1 | 2 | 1 |
Construct histograms for following frequency distribution:
| Class Interval | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 |
| Frequency | 11 | 23 | 30 | 20 | 16 |
The time taken, in seconds, to solve a problem for each of 25 persons is as follows:
| 16 | 20 | 26 | 27 | 28 |
| 30 | 33 | 37 | 38 | 40 |
| 42 | 43 | 46 | 46 | 47 |
| 48 | 49 | 50 | 53 | 58 |
| 59 | 60 | 64 | 52 | 20 |
(i) Construct a frequency distribution for these data using a class interval of 10 seconds.
(ii) In a school the weekly pocket money of 50 students is as follow's:
| Weekly pocket money (₹) | No. of student |
| 40 - 50 | 2 |
| 59 - 60 | 8 |
| 60 - 70 | 12 |
| 70 - 80 | 14 |
| 80 - 90 | 8 |
| 90 - 100 | 6 |
Draw a histogram and a frequency polygon on the same graph. Find mode from the graph.
(Use a graph paper for this question.) The daily pocket expenses of 200 students in a school are given below:
| Pocket expenses (in ₹) |
Number of students (frequency) |
| 0 - 5 | 10 |
| 5 - 10 | 14 |
| 10 - 15 | 28 |
| 15 - 20 | 42 |
| 20 - 25 | 50 |
| 25 - 30 | 30 |
| 30 - 35 | 14 |
| 35 - 40 | 12 |
Draw a histogram representing the above distribution and estimate the mode from the graph.
Identify the following data can be represented in a histogram?
The number of mountain climbers in the age group 20 to 60 in Tamil Nadu.
Identify the following data can be represented in a histogram?
The number of students in each class of a school
In a village, there are 570 people who have cell phones. An NGO survey their cell phone usage. Based on this survey a histogram is drawn
How many people use the cell phone for less than 3 hours?
Draw a histogram for the following data.
| Class Interval | 0 − 10 | 10 − 20 | 20 − 30 | 30 − 40 | 40 − 50 | 50 − 60 |
| No. of students | 5 | 15 | 23 | 20 | 10 | 7 |
Construct a histogram from the following distribution of total marks of 40 students in a class.
| Marks | 90 − 110 | 110 − 130 | 130 − 150 | 150 − 170 | 170 − 190 | 190 − 210 |
| No. of Students | 9 | 5 | 10 | 7 | 4 | 6 |
Histogram is a graph of a ________ frequency distribution
Form a continuous frequency distribution table and draw histogram from the following data.
| Age (in years) | No. of persons |
| Under 5 | 1 |
| Under 10 | 12 |
| Under 15 | 19 |
| Under 20 | 26 |
| Under 25 | 27 |
| Under 30 | 35 |
| Under 35 | 38 |
| Under 40 | 45 |
| Under 45 | 48 |
| Under 50 | 53 |
Try yourself
- Next time when you watch your favourite TV programme, count the number of advertisements during each break. Use tally marks. Put a dot below the tally when you find children in any advertisement.
- Compare with your friends. Do you get different answers?
In a histogram ______ are drawn with width equal to a class interval without leaving any gap in between.
Show the following data by a frequency polygon:
| Electricity bill (₹) | Families |
| 200 – 400 | 240 |
| 400 – 600 | 300 |
| 600 – 800 | 450 |
| 800 – 1000 | 350 |
| 1000 – 1200 | 160 |
The table given below shows the runs scored by a cricket team during the overs of a match.
| Overs | Runs scored |
| 20 – 30 | 37 |
| 30 – 40 | 45 |
| 40 – 50 | 40 |
| 50 – 60 | 60 |
| 60 – 70 | 51 |
| 70 – 80 | 35 |
Use graph sheet for this question.
Take 2 cm = 10 overs along one axis and 2 cm = 10 runs along the other axis.
- Draw a histogram representing the above distribution.
- Estimate the modal runs scored.
