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Question
There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics.
70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47
By taking classes 30-40, 40-50 ... prepare equal to or more than type cumulative frequency table and answer the following questions based on it.
- How many students have scored marks 70 or more than 70?
- How many students have scored marks 30 or more than 30?
Solution
The marks scored by 68 students of 9th standard from Model Highschool, Nandpur out of 80, in the written exam of mathematics are as follows:
70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47
| Class (Marks) | Frequency | equal to or more than type cumulative frequency |
| 30 - 40 | 14 | 68 |
| 40 - 50 | 20 | 68 − 14 = 54 |
| 50 - 60 | 11 | 54 − 20 = 34 |
| 60 - 70 | 12 | 34 − 11 = 23 |
| 70 - 80 | 9 | 23 − 12 = 11 |
| 80 - 90 | 2 | 11 − 9 = 2 |
| Total N = 68 |
- The number of students who have scored marks 70 or more than 70 is 11.
-
The number of students who have scored marks 30 or more than 30 is 68.
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Frequency (No. of students) |
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| 150 - 153 | 05 | 05 |
| 153 - 156 | 07 | 05 + `square` = `square` |
| 156 - 159 | 15 | `square` + 15 = `square` |
| 159 - 162 | 10 | `square` + `square` = 37 |
| 162 - 165 | 05 | 37 + 5 = 42 |
| 165 - 168 | 03 | `square` + `square` = 45 |
| Total N = 45 |
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| Class (Monthly income in Rs.) |
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| 1000 - 5000 | 45 | ______ |
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The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare frequency distribution table and cumulative frequency table more than or equal to type.
55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.
- How many students obtained marks 40 or above 40?
- How many students obtained marks 90 or above 90?
- How many students obtained marks 60 or above 60?
- What is the cumulative frequency of equal to or more than type of the class 0-10?
The data is given for 62 students in a certain class regarding their mathematics marks out of 100. Take the classes 0-10, 10-20.. and prepare less than type cumulative frequency table and answer the following questions.
55, 60, 81, 90, 45, 65, 45, 52, 30, 85, 20, 10, 75, 95, 09, 20, 25, 39, 45, 50, 78, 70, 46, 64, 42, 58, 31, 82, 27, 11, 78, 97, 07, 22, 27, 36, 35, 40, 75, 80, 47, 69, 48, 59, 32, 83, 23, 17, 77, 45, 05, 23, 37, 38, 35, 25, 46, 57, 68, 45, 47, 49.
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- How many students obtained less than 10 marks?
- How many students obtained less than 60 marks?
- Find the cumulative frequency of the class 50-60.
From following table, what is the cumulative frequency of less than type for the class 30-40?
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Frequency | 7 | 3 | 12 | 13 | 2 |
There are 68 students of 9th standard from model Highschool, Nandpur. They have scored following marks out of 80, in written exam of mathematics.
70, 50, 60, 66, 45, 46, 38, 30, 40, 47, 56, 68, 80, 79, 39, 43, 57, 61, 51, 32, 42, 43, 75, 43, 36, 37, 61, 71, 32, 40, 45, 32, 36, 42, 43, 55, 56, 62, 66, 72, 73, 78, 36, 46, 47, 52, 68, 78, 80, 49, 59, 69, 65, 35, 46, 56, 57, 60, 36, 37, 45, 42, 70, 37, 45, 66, 56, 47
By taking classes 30-40, 40-50, .... prepare the less than type cumulative frequency table
- How many students, have scored marks less than 80?
- How many students have scored marks less than 40?
- How many students have scored marks less than 60?
Prepare a cumulative frequency distribution table of the marks scored by 60 students in a test are given below:
| Marks | No. of students |
| 0 - 10 | 4 |
| 10 20 | 15 |
| 20 - 30 | 21 |
| 30 - 40 | 12 |
| 40 50 | 8 |
The table given below shows the ages of patients being treated in a hospital. Construct a cumulative frequency distribution table for the same:
| Age | No. of patients |
| 10 - 20 | 90 |
| 20 - 30 | 50 |
| 30 - 40 | 60 |
| 40 - 50 | 80 |
| 50 - 60 | 50 |
| 60 - 70 | 30 |
The electricity bills of 45 houses in a particular locality are given below. Tabulate the given data and present it as a cumulative frequency table with one of the classes being 300 - 450:
784, 567, 890, 231, 150, 458, 356, 762, 386, 824, 525, 663, 724, 841, 315, 641, 156, 715, 156, 317, 814, 547, 879, 456, 463, 664, 175, 584, 515, 487, 871, 511, 522, 454, 247, 819, 412, 326, 445, 311, 321, 545, 344, 266, 351.
Construct a frequency distribution table from the given cumulative frequency distribution showing the weights of 750 students in a school:
| Weight (in kg) | c.f. |
| More Than 25 | 750 |
| More Than 30 | 640 |
| More Than 35 | 615 |
| More Than 40 | 485 |
| More Than 45 | 370 |
| More Than 50 | 220 |
| More Than 55 | 124 |
| More Than 60 | 49 |
| More Than 65 | 24 |
| More Than 70 | 0 |
a. Find the number of students whose weight lie in the interval 40-45
b. Find the interval which has the most number of students.
