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Question
Draw the Histogram and hence, the frequency polygon for the following frequency distribution:
| House Rent (In ₹ per month) | 400-600 | 600-800 | 800-1000 | 1000-1200 |
| Number of families | 200 | 240 | 300 | 50 |
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Solution
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For which of these would you use a histogram to show the data?
(a) The number of letters for different areas in a postman’s bag.
(b) The height of competitors in an athletics meet.
(c) The number of cassettes produced by 5 companies.
(d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station.
Give reasons for each.
The weekly wages (in Rs) of 30 workers in a factory are.
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840
Using tally marks make a frequency table with intervals as 800 − 810, 810 − 820 and so on.
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| Class Marks | 16 | 24 | 32 | 40 | 48 | 56 | 64 |
| Frequency | 8 | 12 | 15 | 18 | 25 | 19 | 10 |
Given below is the frequency distribution of the heights of 50 students of a class:
| Class interval: | 140−145 | 145−150 | 150−155 | 155−160 | 160−165 |
| Frequency: | 8 | 12 | 18 | 10 | 5 |
Draw a histogram representing the above data.
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 |
Below is the histogram depicting marks obtained by 43 students of a class:
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The weekly wages (in Rs.) of 30 workers in a factory are given:
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Mark a frequency table with intervals as 800-810, 810-820 and so on, using tally marks. Also, draw a histogram and answer the following questions:
(i) Which group has the maximum number of workers?
(ii) How many workers earn Rs 850 and more?
(iii) How many workers earn less than Rs 850?
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 | 110-119 | 120-129 | 130-139 | 140-149 | 150-159 |
| Frequency | 15 | 23 | 30 | 20 | 16 |
Construct a frequency polygon without using a histogram for the following frequency distribution :
| Class Interval | 10-20 | 20-40 | 40-60 | 60-80 | 80-100 |
| Frequency | 9 | 17 | 15 | 20 | 14 |
Construct a frequency polygon without using a histogram for the following frequency distribution :
| Class Mark | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
| Frequency | 4 | 20 | 40 | 45 | 30 | 25 | 5 |
Draw a histogram and frequency polygon to represent the following data (on the same scale) which shows the monthly cost of living index of a city in a period of 2 years:
| Cost of living Index | Number of months |
| 440 - 460 | 2 |
| 460 - 480 | 4 |
| 480 - 500 | 3 |
| 500 - 520 | 5 |
| 520 - 540 | 3 |
| 540 - 560 | 2 |
| 560 - 580 | 1 |
| 580 - 600 | 4 |
| Total | 24 |
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 of them use the cell phone for more than 5 hours?
Histogram is a graph of a ________ frequency distribution
Histogram shows the number of people owning the different number of books. Answer the question based on it.
The total number of people surveyed is ______.
Histogram shows the number of people owning the different number of books. Answer the question based on it.
The number of people owning books more than 60 is ______.
Histogram shows the number of people owning the different number of books. Answer the question based on it.
The number of people owning books less than 40 is ______.
From the histogram given on the right, we can say that 1500 males above the age of 20 are literate.
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 given graph with a histogram represents the number of plants of different heights grown in a school campus. Study the graph carefully and answer the following questions:
- Make a frequency table with respect to the class boundaries and their corresponding frequencies.
- State the modal class.
- Identify and note down the mode of the distribution.
- Find the number of plants whose height range is between 80 cm to 90 cm.
