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S Chand Class 10 ICSE Maths Solutions Chapter 19 Histogram and Ogive Ex 19(b)
Question 1.
| Class-interval | 0-10 | 10-20 | 20-30 | 30-40 |
| Frequency | 10 | 45 | 12 | 3 |
Solution:
| Class-interval | Frequency |
| 0-10 | 10 |
| 10-20 | 45 |
| 20-30 | 12 |
| 30-40 | 3 |
Represent class-intervals along x-axis and frequency along y-axis and draw the histogram as shown here Now inside the highest rectangle we join A to C and B to D intersecting each other at P.
From P, draw PQ perpendicular on x-axis meeting it at Q, then Q is the mode which is 15 (approx)
Question 2.
| Marks | 1-5 | 6-10 | 11-15 | 16-20 | 21-25 |
| f | 7 | 10 | 16 | 32 | 24 |
Solution:
Writing the classes in exclusive form,
| Marks | f |
| 0.5-5.5 | 7 |
| 5.5-10.5 | 10 |
| 10.5-15.5 | 16 |
| 15.5-20.5 | 32 |
| 20.5-25.5 | 24 |
Represent the marks (class interval) along x-axis and f along y-axis and draw the histogram as shown. Now inside the highest rectangle. Join A to C and B to D intersecting each other at P Through P, draw PQ perpendicular on x-axis meeting it at Q, Then Q is the mode which is 18.8 = 19 (approx)
Hence mode = 19 (approx)
Question 3.
| Marks | 26-30 | 31-35 | 36-40 | 41-45 |
| f | 18 | 10 | 5 | 1 |
Solution:
Writing the classes in exclusive form
| Marks | f |
| 25.5-30.5 | 18 |
| 30.5-35.5 | 10 |
| 35.5-40.5 | 5 |
| 40.5-45.5 | 1 |
Represent marks along x-axis and f along y-axis and draw the histogram as shown. Now inside the highest rectangle, join A to C and B to D which intersect each other at P. Through P, draw PQ perpendicular to x-axis meeting x-axis at Q.
∴ Q is the mode which is 29 (approx)
∴ Mode = 29 (approx)
Question 4.
| Mid-value | 60 | 64 | 68 | 72 | 76 |
| Frequency | 25 | 8 | 10 | 6 | 4 |
Solution:
∵ Mid value of each class is given
∴ Forming the classes, with these mid values, we get 58-62, 62-66, 66-70, 70-74 and 74-78
| Class | Frequency |
| 58-62 | 25 |
| 62-66 | 8 |
| 66-70 | 10 |
| 70-74 | 6 |
| 74-78 | 4 |
Represent classes along x-axis and frequency along y-axis and draw the histogram as shown. Now inside the highest rectangle, join A to C and B to D intersecting each other at P. Through P, draw PQ perpendicular on x-axis.
Q is the mode which is 60.4 = (approx)
∴ Mode = 60 (approx)
Question 5.
Draw a histogram from the following data and measure the modal value :
(a)
| Size class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Frequency | 5 | 11 | 19 | 21 | 16 | 10 |
(b)
| Size class | 60-70 | 70-80 | 80-90 | 90-100 | ||
| Frequency | 8 | 6 | 3 | 1 |
Solution:
(a) Taking size class along x-axis and frequency along y-axis, and draw the histogram as shown
∴ Mode = 33 (approx)
(b) Taking size class along x-axis and frequency along y-axis, and draw the histogram as shown
Now inside the highest rectangle, join A to C and B to D intersecting each other at P. Through P, draw PQ perpendicular to x-axis. Q is mode which is 68 (approx)
∴ Mode = 68 (approx)