Students often turn to S Chand Class 9 Maths Solutions ICSE Chapter 15 Mean, Median and Frequency Polygon Ex 15(C) to clarify doubts and improve problem-solving skills.
S Chand Class 9 ICSE Maths Solutions Chapter 15 Mean, Median and Frequency Polygon Ex 15(C)
Question 1.
In a class of 60 boys, the marks obtained in a monthly test were as under :
| Marks | Students |
| 10-20 | 10 |
| 20-30 | 25 |
| 30-40 | 12 |
| 40-50 | 08 |
| 50-60 | 05 |
Draw a frequency polygon to represents the above data.
Solution:
| Marks | Mid-point | Students |
| 10-20 | 15 | 10 |
| 20-30 | 25 | 25 |
| 30-40 | 35 | 12 |
| 40-50 | 45 | 08 |
| 50-60 | 55 | 05 |
Now plot the points (15, 10), (25, 25), (35, 12), (45, 8) and (55, 5) on the graph and join them and complete the frequency polygon as shown.
Question 2.
Represent the following data by frequency polygon?
| Marks | Students |
| 0-10 | 3 |
| 10-20 | 7 |
| 20-30 | 6 |
| 30-40 | 2 |
| 40-50 | 5 |
Solution:
| Marks | Mid-point | Students |
| 0-10 | 5 | 3 |
| 10-20 | 15 | 7 |
| 20-30 | 25 | 6 |
| 30-40 | 35 | 2 |
| 40-50 | 45 | 5 |
Now plot the points (5, 3), (15, 7), (25, 6), (35, 2) and (45, 5) on the graph and join them and complete the frequency polygon as shown.
Question 3.
| Class | Frequency |
| 20-29 | 7 |
| 30-39 | 3 |
| 40-49 | 5 |
| 50-59 | 2 |
| 60-69 | 5 |
Solution:
| Class | Mid-point | Frequency |
| 20-29 | 25 | 7 |
| 30-39 | 35 | 3 |
| 40-49 | 45 | 5 |
| 50-59 | 55 | 2 |
| 60-69 | 65 | 5 |
Now plot the points (25, 7), (35, 3), (45, 5), (55, 2) and (65, 5) on the graph and join them and complete the frequency polygon as shown.
Question 4.
Rohit asked people to draw a line 5 cm long using a straight edge without any markings on it. Here are the lengths in centimetres of the lines drawn :
4.3 3.2 3.9 4.7 5.8 6.1 5.7 6.2 6.5 3.7 4.2 5.1 6.5 7.2 7.4 3.7 5.8 4.2 4.1 5.0 5.1 4.7 3.2 3.5 5.2 2.9 2.8 4.3 5.1 4.8
(a) Draw up a grouped frequency table for the data. Use a class interval of 1 centimetre.
(b) Draw a frequency polygon for the data.
Solution:
Highest length = ?
Lowest length = 7.4
Now plot the points (2.5, 2), (3.5, 6), (4.5, 8), (5.5, 8), (6.5, 4) and (7.5, 2) on the graph and join them and complete the frequency polygon as shown.
Question 5.
For the following data, draw a histogram and a frequency polygon.
| Age (in years) | No. of persons |
| 0-6 | 6 |
| 6-12 | 11 |
| 12-18 | 25 |
| 18-24 | 35 |
| 24-30 | 18 |
| 30 – 36 | 12 |
| 36-42 | 6 |
Solution:
| Age (in years) | No. of persons (f) |
| 0-6 | 6 |
| 6-12 | 11 |
| 12-18 | 25 |
| 18-24 | 35 |
| 24-30 | 18 |
| 30 – 36 | 12 |
| 36-42 | 6 |
Represent age along x-axis and no. of persons on y-axis and complete the histogram. By joining the mid-points of each histogram in order, we get as shown here.
