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Question
Construct a histogram for the following data:
| Monthly school fee (in Rs): | 30−60 | 60−90 | 90−120 | 120−150 | 150−180 | 180−210 | 210−240 |
| Number of schools: | 5 | 12 | 14 | 18 | 10 | 9 | 4 |
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Solution
The class limits are represented along the x-axis and the frequencies along the y-axis on a suitable scale. Taking class intervals as bases and corresponding frequencies as heights of the rectangles, the histogram of the given data can be obtained as shown in the figure below:
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| Electricity bill (₹) | 0 - 200 | 200 - 400 | 400 - 600 | 600 - 800 | 800 - 1000 |
| Families | 240 | 300 | 450 | 350 | 160 |
Number of workshops organized by a school in different areas during the last five years are as follows:
| Years | No. of workshops |
| 1995−1996 | 25 |
| 1996−1997 | 30 |
| 1997−1998 | 42 |
| 1998−1999 | 50 |
| 1999−2000 | 65 |
Draw a histogram representing the above data.
Draw a histogram for the daily earnings of 30 drug stores in the following table:
| Daily earnings (in Rs): | 450−500 | 500−550 | 550−600 | 600−650 | 650−700 |
| Numbers of stores: | 16 | 10 | 7 | 3 | 1 |
The following histogram shows the number of literate females in the age group of 10 to 40 years in a town:
(i) Write the age group in which the number of literate female is the highest.
(ii) What is the class width?
(iii) What is the lowest frequency?
(iv) What are the class marks of the classes?
(v) In which age group literate females are the least?
Below is the histogram depicting marks obtained by 43 students of a class:
(i) Write the number of students getting the highest marks.
(ii) What is the class size?
Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:
| Marks | 25 | 30 | 35 | 40 | 45 | 50 |
| No. of students | 6 | 15 | 12 | 10 | 18 | 9 |
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 |
Distribution of height in cm of 100 people is given below:
| Class interval (cm) | Frequency |
| 145 - 155 | 3 |
| 155 - 165 | 35 |
| 165 - 175 | 25 |
| 175 - 185 | 15 |
| 185 - 195 | 20 |
| 195 - 205 | 2 |
Draw a histogram to represent the above data.
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.
Identify the following data can be represented in a histogram?
The wickets fallen from 1 over to 50th over in a one day cricket match
A graph that displays data that changes continuously over the periods of time is _________
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 |
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The following pictorial representation of data is a histogram.
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.
