Continuous practice using ICSE Class 10 Maths Solutions S Chand Chapter 19 Histogram and Ogive Ex 19(a) can lead to a stronger grasp of mathematical concepts.
S Chand Class 10 ICSE Maths Solutions Chapter 19 Histogram and Ogive Ex 19(a)
Question 1.
Represent the following distribution of ages (in years) of 35 teachers in a school by means of a histogram.
| Age (in years) | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 |
| Number of Teachers | 12 | 11 | 8 | 1 | 3 |
Solution:
| Age (in years) | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 |
| Number of Teachers | 12 | 11 | 8 | 1 | 3 |
Draw the axis and represent the age (in years) along x-axis and number of teachers (frequencies) along y-axis and prepare the histogram as given under.
Question 2.
The weekly observatios on cost of living index in a certain city for a year give the following frequency table :
| Cost of living index | 140-150 | 150-160 | 160-170 | 170-180 | 180-190 | 190-200 |
| Number of weeks | 5 | 10 | 16 | 12 | 7 | 2 |
Draw histogram to represent the data.
Solution:
We represent the cost of living index along x-axis and number of weeks (frequencies) along they- axis and prepare the histogram as given below.
Question 3.
Draw a histogram for daily earning of 20 drug stores given in the following data :
| Daily earnings (in Rs.) | 150-200 | 200-250 | 250-300 | 300-350 |
| Number of stores | 14 | 9 | 3 | 4 |
Solution:
We represent daily earnings in rupees along x-axis and number of stores along y-axis and prepare the histogram as shown in the figure given here.
Draw histograms for the following distributions :
Question 4.
(a)
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| No. of boys | 3 | 7 | 5 | 8 | 2 |
(b)
| Money earned in Rs. | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | 120-140 |
| No. of students | 4 | 18 | 22 | 14 | 10 | 8 | 4 |
(c)
| Class | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 |
| Frequency | 7 | 3 | 5 | 2 | 6 | 4 |
(d)
| Class interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-70 | 70-100 |
| Frequency | 6 | 10 | 16 | 10 | 6 | 3 |
Solution:
(a)
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| No. of boys | 3 | 7 | 5 | 8 | 2 |
We represent marks on the x-axis and number of boys v-axis and prepare the histogram as given here.
(b)
| Money earned (in Rs.) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 | 120-140 |
| No: of students. | 4 | 18 | 22 | 14 | 10 | 8 | 4 |
We represent money earned along x-axis and no. of students on they-axis and prepare the histogram as shown here.
(c)
| Class | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 |
| Frequency | 7 | 3 | 5 | 2 | 6 | 4 |
Arranging in exclusive form.
| Class | 0.5-10.5 | 10.5-20.5 | 20.5-30.5 | 30.5-40.5 | 40.5-50.5 | 50.5-60.5 |
| Frequency | 7 | 3 | 5 | 2 | 6 | 4 |
We represent class along x-axis and frequencies along y-axis and prepare the histogram as shown here.
(d)
| Class interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-70 | 70-100 |
| Frequency | 6 | 10 | 16 | 10 | 6 | 3 |
Here we represent class intervals along x-axis and frequency alongy-axis and prepare the histogram as shown here.
Question 5.
Given below are the marks obtained by 40 students in an examination :
| 29 | 45 | 23 | 30 | 40 | 11 | 48 | 01 | 15 | 35 |
| 40 | 03 | 12 | 48 | 49 | 18 | 30 | 24 | 25 | 29 |
| 31 | 32 | 25 | 22 | 27 | 41 | 12 | 13 | 02 | 44 |
| 07 | 43 | 09 | 49 | 19 | 13 | 32 | 39 | 25 | 03 |
Taking class-intervals 1 – 10, 11 – 20, ………, 41 – 50, make a frequency table for the above distribution and draw a histogram to represent it.
Solution:
We prepare frequency distribution table as given below :
We represent class intervals (exclusive) along x-axis and frequency along y-axis and prepare the histogram to represent the above data as given below :
Question 6.
Present in the form of a frequency table the marks obtained by 50 candidates. Take the class-intervals as 11 – 20; 21 – 30… etc.
| 35 | 56 | 25 | 40 | 38 | 48 | 58 | 43 | 30 | 47 |
| 46 | 45 | 31 | 45 | 56 | 39 | 46 | 47 | 23 | 40 |
| 48 | 50 | 36 | 56 | 35 | 43 | 59 | 40 | 48 | 35 |
| 53 | 57 | 33 | 50 | 23 | 46 | 49 | 57 | 35 | 43 |
| 64 | 40 | 50 | 56 | 36 | 19 | 49 | 52 | 51 | 42 |
Draw a histogram for the above distribution.
Solution:
Lowest data = 19,
Highest data = 64
We prepare frequency distribution table of the given data as given below :
Now we represent exclusive class intervals along x-axis and frequency alongy-axis and prepare a histogram to represent the given data as shown below:
Question 7.
Explain the methods of draw ing histogram and frequency polygon. Following table gives the marks distribution of 160 students in a certain class.
From the above data draw a histogram and frequency polygon.
Solution:
| Class intervals | No. of students
c.f. |
Frequency |
| 5-15 | 160 | 8 |
| 15-25 | 152 | 12 |
| 25-35 | 140 | 15 |
| 35-45 | 125 | 20 |
| 45-55 | 105 | 24 |
| 55-65 | 81 | 32 |
| 65-75 | 49 | 26 |
| 75-85 | 23 | 18 |
| 85-95 | 5 | 5 |
| 95-105 | 0 | 0 |
We present class intervals along x-axis and frequency alongy-axis and prepare the histogram and frequency polygon by joining the mid-points of consecutive class intervals.
Question 8.
The number of match sticks in 40 boxes, on counting was found as given below :
| 44 | 41 | 42 | 43 | 47 | 50 | 51 | 49 | 43 | 42 |
| 40 | 42 | 44 | 45 | 49 | 42 | 46 | 49 | 45 | 49 |
| 45 | 47 | 48 | 43 | 43 | 44 | 48 | 43 | 46 | 50 |
| 43 | 52 | 46 | 49 | 52 | 51 | 47 | 43 | 43 | 45 |
Taking classes 40 – 41, 42 – 43, etc., construct the frequency distribution table for the above data. Draw a histogram to represent the above distribution.
Solution:
Highest score = 52, lowest score = 40
Now we prepare the frequency distribution table in exclusive form
Now we represent classes along x-axis and frequencies along v-axis and prepare the histogram representing the given data :
