Exercise 7.6 primarily discusses the relationship among mean, median and mode, as well as constructing a cumulative frequency polygon(OGIVE). Problems in this exercise are well crafted to understand the two types of ogives and their applications. Students wanting to get an edge over these concepts can access the RD Sharma Solutions Class 10. Get the RD Sharma Solutions for Class 10 Maths Chapter 7 Statistics Exercise 7.6 PDF is provided below for further assistance when solving this exercise.
RD Sharma Solutions for Class 10 Maths Chapter 7 Statistics Exercise 7.6
Access RD Sharma Solutions for Class 10 Maths Chapter 7 Statistics Exercise 7.6
1. Draw an ogive by less than the method for the following data:
| No. of rooms | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of houses | 4 | 9 | 22 | 28 | 24 | 12 | 8 | 6 | 5 | 2 |
Solution:
| No. of rooms | No. of houses | Cumulative Frequency |
| Less than or equal to 1 | 4 | 4 |
| Less than or equal to 2 | 9 | 13 |
| Less than or equal to 3 | 22 | 35 |
| Less than or equal to 4 | 28 | 63 |
| Less than or equal to 5 | 24 | 87 |
| Less than or equal to 6 | 12 | 99 |
| Less than or equal to 7 | 8 | 107 |
| Less than or equal to 8 | 6 | 113 |
| Less than or equal to 9 | 5 | 118 |
| Less than or equal to 10 | 2 | 120 |
It’s required to plot the points (1, 4), (2, 13), (3, 35), (4, 63), (5, 87), (6, 99), (7, 107), (8, 113), (9, 118), (10, 120), by taking upper-class limit over the x-axis and cumulative frequency over the y-axis.
2. The marks scored by 750 students in an examination are given in the form of a frequency distribution table:
| Marks | No. of Students |
| 600 – 640 | 16 |
| 640 – 680 | 45 |
| 680 – 720 | 156 |
| 720 – 760 | 284 |
| 760 – 800 | 172 |
| 800 – 840 | 59 |
| 840 – 880 | 18 |
Prepare a cumulative frequency distribution table by less than method and draw an ogive.
Solution:
| Marks | No. of Students | Marks Less than | Cumulative Frequency |
| 600 – 640 | 16 | 640 | 16 |
| 640 – 680 | 45 | 680 | 61 |
| 680 – 720 | 156 | 720 | 217 |
| 720 – 760 | 284 | 760 | 501 |
| 760 – 800 | 172 | 800 | 673 |
| 800 – 840 | 59 | 840 | 732 |
| 840 – 880 | 18 | 880 | 750 |
Plot the points (640, 16), (680, 61), (720, 217), (760, 501), (800, 673), (840, 732), (880, 750) by taking upper class limit over the x-axis and cumulative frequency over the y-axis.
3. Draw an Ogive to represent the following frequency distribution:
| Class-interval | 0 – 4 | 5 – 9 | 10 – 14 | 15 – 19 | 20 – 24 |
| No. of students | 2 | 6 | 10 | 5 | 3 |
Solution:
Since the given frequency distribution is not continuous, we will have to first make it continuous and then prepare the cumulative frequency:
| Class-interval | No. of Students | Less than | Cumulative frequency |
| 0.5 – 4.5 | 2 | 4.5 | 2 |
| 4.5 – 9.5 | 6 | 9.5 | 8 |
| 9.5 – 14.5 | 10 | 14.5 | 18 |
| 14.5 – 19.5 | 5 | 19.5 | 23 |
| 19.5 – 24.5 | 3 | 24.5 | 26 |
Plot the points (4.5, 2), (9.5, 8), (14.5, 18), (19.5, 23), (24.5, 26) by taking the upper-class limit over the x-axis and cumulative frequency over the y-axis.
4. The monthly profits (in Rs) of 100 shops are distributed as follows:
| Profit per shop | No of shops: |
| 0 – 50 | 12 |
| 50 – 100 | 18 |
| 100 – 150 | 27 |
| 150 – 200 | 20 |
| 200 – 250 | 17 |
| 250 – 300 | 6 |
Draw the frequency polygon for it.
Solution:
Doing for the less than method, we have
| Profit per shop | Mid-value | No of shops: |
| Less than 0 | 0 | 0 |
| Less than 0 – 50 | 25 | 12 |
| Less than 50 – 100 | 75 | 18 |
| Less than 100 – 150 | 125 | 27 |
| Less than 150 – 200 | 175 | 20 |
| Less than 200 – 250 | 225 | 17 |
| Less than 250 – 300 | 275 | 6 |
| Above 300 | 300 | 0 |
By plotting the coordinates respectively, we can get the frequency polygon.
5. The following distribution gives the daily income of 50 workers of a factory:
| Daily income (in Rs): | No of workers: |
| 100 – 120 | 12 |
| 120 – 140 | 14 |
| 140 – 160 | 8 |
| 160 – 180 | 6 |
| 180 – 200 | 10 |
Convert the above distribution to a ‘less than’ type cumulative frequency distribution and draw its ogive.
Solution:
Firstly, we prepare the cumulative frequency table by less than method as given below:
| Daily income | Cumulative frequency |
| Less than 120 | 12 |
| Less than 140 | 26 |
| Less than 160 | 34 |
| Less than 180 | 40 |
| Less than 200 | 50 |
Now we mark on the x-axis upper class limit, y-axis cumulative frequencies. Thus we plot the point (120, 12), (140, 26), (160, 34), (180, 40), (200, 50).
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