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The marks scored by students in Mathematics in a certain Examination are given below:

Marks Scored | Number of Students |

0 — 20 | 3 |

20 — 40 | 8 |

40 — 60 | 19 |

60 — 80 | 18 |

80 — 100 | 6 |

Draw histogram for the above data.

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#### Solution

#### RELATED QUESTIONS

Given below is the frequency distribution of driving speeds (in km/hour) of the vehicles of 400 college students:

Speed (in km/hr) | No. of Students |

20-30 | 6 |

30-40 | 80 |

40-50 | 156 |

50-60 | 98 |

60-70 |
60 |

Draw Histogram and hence the frequency polygon for the above data.

The following is the frequency distribution of waiting time at ATM centre; draw histogram to represent the data:

Waiting time(in seconds) |
Number ofCustomers |

0 -30 | 15 |

30 - 60 | 23 |

60 - 90 | 64 |

90 - 120 | 50 |

120 - 150 | 5 |

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 shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning

W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W

Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

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.

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?

The histogram below represents the scores obtained by 25 students in a mathematics mental test. Use the data to :

1) Frame a frequency distribution table

2) To calculate mean

3) To determine the Modal class

A Mathematics aptitude test of 50 students was recorded as follows:

Marks | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 – 100 |

No. of Students | 4 | 8 | 14 | 19 | 5 |

Draw a histogram from the above data using a graph paper and locate the mode.

Draw histogram ffor the following distributtions:

Class Marks |
16 | 24 | 32 | 40 | 48 | 56 | 64 |

Frequency |
8 | 12 | 15 | 18 | 25 | 19 | 10 |

Draw a histogram of the following data.

Height of student (cm) | 135 - 140 | 140 - 145 | 145 - 150 | 150 - 155 |

No. of students | 4 | 12 | 16 | 8 |

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?

Result (Percentage) | 30 - 40 | 40 - 50 | 50 - 60 | 60 -70 | 70 - 80 | 80 - 90 | 90 - 100 |

No. of students | 7 | 33 | 45 | 65 | 47 | 18 | 5 |

Find the correct answer from the alternatives given.

No. of trees planted by each student |
1 - 3 | 4 - 6 | 7 - 9 | 10 - 12 |

No. of students | 7 | 8 | 6 | 4 |

The above data is to be shown by a frequency polygon. The coordinates of the points to show number of students in the class 4-6 are . . . .

The age groups and the number of persons in the age groups, who donated blood in blood donation camp is given below. Find the measures of central angles to show the information by a pie diagram.

Age group (Years) | 20-25 | 25-30 | 30-35 | 35-40 |

No of persons | 80 | 60 | 35 | 25 |

The following table shows the investment made by some families. Show

the information by a histogran.

Investment (Thousand Rupees) |
10-15 | 15-20 | 20-25 | 25-30 | 30-35 |

No. of families | 30 | 50 | 60 | 55 | 15 |

The following table is based on the marks of the first term examination of 10th class students. Show the information by a histogram. Also, draw a frequency polygon with the help of the histogram.

Class-mark of marks | 325 | 375 | 425 | 475 | 525 | 575 |

No. of students | 25 | 35 | 45 | 40 | 32 | 20 |

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 |

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.

In a hypothetical sample of 20 people the amounts of money with them were found to be as follows:

114, 108, 100, 98, 101, 109, 117, 119, 126, 131, 136, 143, 156, 169, 182, 195, 207, 219, 235, 118.

Draw the histogram of the frequency distribution (taking one of the class intervals as 50−100).

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?

The following histogram shows the monthly wages (in Rs) of workers in a factory:

(i) In which wage-group the largest number of workers are being kept? What is their number?

(ii) What wages are the least number of workers getting? What is the number of such workers?

(iii) What is the total number of workers?

(iv) What is the factory size?

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?

The weekly wages (in Rs.) of 30 workers in a factory are given:

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

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?

The following frequency distribution table shows marks obtained by 180 students in Mathematics examination

Marks |
No .of. students |

0 – 10 | 25 |

10 – 20 | x |

20 – 30 |
30 |

30 – 40 | 2x |

40 – 50 | 65 |

Find the value of x.

Also draw a histogram representing the above information.

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 |

Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:

Shoe size |
5 | 6 | 7 | 8 | 9 | 10 | 11 |

Frequency |
8 | 1 | 7 | 14 | 11 | 5 | 4 |

Construct histograms for following frequency distribution:

Class Interval |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |

Frequency |
8 | 20 | 34 | 22 | 10 | 6 |

Construct a frequency polygon without using a histogram for the following frequency distribution :

Class Interval |
1-10 | 11-20 | 21-30 | 31-40 | 41-50 |

Frequency |
8 | 12 | 10 | 16 | 6 |

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 |

Represent the following data by histogram:

Price of sugar Per kg (in Rs) | Number of weeks |

28-30 | 4 |

30-32 | 8 |

32-34 | 22 |

34-36 | 12 |

36-38 | 6 |

Draw histogram and hence the frequency polygon for the following frequency distribution:

Rainfall (in cm) | No. of years |

20-25 | 2 |

25-30 | 5 |

30-35 | 8 |

35-40 | 12 |

40-45 | 10 |

45-50 | 7 |

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 |

Following table present educational level (middle stage) of females in Arunachal pradesh according to 1981 census:

Age group |
Number of females (to the nearest ten) |

10 - 14 | 300 |

15 - 19 | 980 |

20 - 24 | 800 |

25 - 29 | 380 |

30 - 34 | 290 |

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.

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 |

Draw the histogram for the following frequency distribution and hence estimate the mode for the distribution.

Class |
Frequency |

0 - 5 | 2 |

5 - 10 | 7 |

10 - 15 | 18 |

15 - 20 | 10 |

20 - 25 | 8 |

25 - 30 | 5 |

Total |
24 |

Draw a histogram to represent the following data:

Pocket money in ₹ |
No. of Students |

150 - 200 | 10 |

200 - 250 | 5 |

250 - 300 | 7 |

300 - 350 | 4 |

350 - 400 | 3 |

(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 votes polled from 7 am to 6 pm in an election

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

The total area of the histogram is _________ to the total frequency of the given data

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?

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

Are people using cell phone for less than 1 hour?

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 |

The marks obtained by 50 students in Mathematics are given below.

(i) Make a frequency distribution table taking a class size of 10 marks

(ii) Draw a histogram and a frequency polygon.

52 | 33 | 56 | 52 | 44 | 59 | 47 | 61 | 49 | 61 |

47 | 52 | 67 | 39 | 89 | 57 | 64 | 58 | 63 | 65 |

32 | 64 | 50 | 54 | 42 | 48 | 22 | 37 | 59 | 63 |

36 | 35 | 48 | 48 | 55 | 62 | 74 | 43 | 41 | 51 |

08 | 71 | 30 | 18 | 43 | 28 | 20 | 40 | 58 | 49 |

Draw a histogram for the following data.

Mid Value (x) |
15 | 25 | 35 | 45 | 55 | 65 | 75 |

Frequency (f) |
12 | 24 | 30 | 18 | 26 | 10 | 8 |

**Represent the following data by histogram:**

Price of Sugar (per kg in ₹) |
Number of Weeks |

18 – 20 | 4 |

20 – 22 | 8 |

22 – 24 | 22 |

24 – 26 | 12 |

26 – 28 | 6 |

28 – 30 | 8 |

**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?

The number of people owning books more than 60 is ______.

From the histogram given on the right, we can say that 1500 males above the age of 20 are literate.

The following pictorial representation of data is a histogram.

Draw a histogram to represent the frequency distribution in question 91.

Prepare a histogram from the frequency distribution table obtained in question 93.

Draw a histogram for the following data.

Class interval |
10 – 15 | 15 – 20 | 20 – 25 | 25 – 30 | 30 – 35 | 35 – 40 |

Frequency |
30 | 98 | 80 | 58 | 29 | 50 |

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 following table shows the classification of percentage of marks of students and the number of students. Draw frequency polygon from the table without drawing histogram:

Result (Percentage) |
Number of Students |

20 - 40 | 25 |

40 - 60 | 65 |

60 - 80 | 80 |

80 - 100 | 15 |

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.