(1) Complete the following cumulative freuqency table:
| Class (Height in cm) |
Frequency (No. of students) |
Less than type frequency |
| 150 - 153 | 05 | 5 |
| 153 - 156 | 07 | 5 + = |
| 156 - 159 | 15 | + 15 = |
| 159 - 162 | 10 | + = 37 |
| 162 - 165 | 05 | 37 + 5 = 42 |
| 165 - 168 | 03 | + = 45 |
Solution:
The Completed table is given below:
| Class (Height in cm) |
Frequency (No. of students) |
Less than type frequency |
| 150 - 153 | 05 | 5 |
| 153 - 156 | 07 | 5 + 7 = 12 |
| 156 - 159 | 15 | 12 + 15 = 27 |
| 159 - 162 | 10 | 27 + 10 = 37 |
| 162 - 165 | 05 | 37 + 5 = 42 |
| 165 - 168 | 03 | 42 + 3 = 45 |
(2) Complete the following Cumulative Frequency Table:
| Class (Monthly Income in ₹) |
Frequency (No. of individuals) |
More than or equal to type cumulative frequency |
| 1000 - 5000 | 45 | ...... |
| 5000 - 10000 | 19 | ...... |
| 10000 - 15000 | 16 | ...... |
| 15000 - 20000 | 02 | ...... |
| 20000 - 25000 | 05 | ...... |
| Total N = 87 |
Solution:
The completed table is given below:
| Class (Monthly Income in ₹) |
Frequency (No. of individuals) |
More than or equal to type cumulative frequency |
| 1000 - 5000 | 45 | 87 |
| 5000 - 10000 | 19 | 87 − 45 = 42 |
| 10000 - 15000 | 16 | 42 − 19 = 23 |
| 15000 - 20000 | 02 | 23 − 16 = 7 |
| 20000 - 25000 | 05 | 7 − 2 = 5 |
| Total N = 87 |
(3) 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
Solution:
The cumulative frequency table (More than or equal to type) is given below:
| Class | Tally Marks | Frequency (f) | Cumulative Frequency (More than type) |
| 0 - 10 | \(|||\) | 3 | 62 |
| 10 - 20 | \(|||\) | 3 | 62 − 3 = 59 |
| 20 - 30 | \(\enclose{downdiagonalstrike}{||||} ||||\) | 9 | 59 − 3 = 56 |
| 30 - 40 | \(\enclose{downdiagonalstrike}{||||} ||||\) | 9 | 56 − 9 = 47 |
| 40 - 50 | \(\enclose{downdiagonalstrike}{||||}\enclose{downdiagonalstrike}{||||} |||\) | 13 | 47 − 9 = 38 |
| 50 - 60 | \(\enclose{downdiagonalstrike}{||||} |\) | 6 | 38 − 13 = 25 |
| 60 - 70 | \(\enclose{downdiagonalstrike}{||||}\) | 5 | 25 − 6 = 19 |
| 70 - 80 | \(\enclose{downdiagonalstrike}{||||} |\) | 6 | 19 − 5 = 14 |
| 80 - 90 | \(\enclose{downdiagonalstrike}{||||}\) | 5 | 14 − 6 = 8 |
| 90 - 100 | \(|||\) | 3 | 8 − 5 = 3 |
| \(\displaystyle N = \sum{f} = 62\) |
Now, answer the following questions:
(i) How many students obtained 40 marks or above 40?
Answer: 38
(ii) How many students obtained marks 90 or above 90?
Answer: 3
(iii) How many students obtained marks 60 or above 60?
Answer: 19
(iv) What is the cumulative frequency of equal to or more than type of the class 0 - 10?
Answer: 62
(4) Using the data in example (3) above, prepare less than type cumulative frequency table and answer the following questions:
Solution:
The cumulative frequency table (Less than or equal to type) is given below:
| Class | Tally Marks | Frequency (f) | Cumulative Frequency (Less than type) |
| 0 - 10 | \(|||\) | 3 | 3 |
| 10 - 20 | \(|||\) | 6 | 3 + 3 = 6 |
| 20 - 30 | \(\enclose{downdiagonalstrike}{||||} ||||\) | 9 | 6 + 9 = 15 |
| 30 - 40 | \(\enclose{downdiagonalstrike}{||||} ||||\) | 9 | 15 + 9 = 24 |
| 40 - 50 | \(\enclose{downdiagonalstrike}{||||}\enclose{downdiagonalstrike}{||||} |||\) | 13 | 24 + 13 = 37 |
| 50 - 60 | \(\enclose{downdiagonalstrike}{||||} |\) | 6 | 37 + 6 = 43 |
| 60 - 70 | \(\enclose{downdiagonalstrike}{||||}\) | 5 | 43 + 5 = 48 |
| 70 - 80 | \(\enclose{downdiagonalstrike}{||||} |\) | 6 | 48 + 6 = 54 |
| 80 - 90 | \(\enclose{downdiagonalstrike}{||||}\) | 5 | 54 + 5 = 59 |
| 90 - 100 | \(|||\) | 3 | 59 + 3 = 62 |
| \(\displaystyle N = \sum{f} = 62\) |
Now, answer the following questions:
(i) How many students obtained less than 40 marks?
Answer: 24
(ii) How many students obtained less than 10 marks?
Answer: 3
(iii) How many students obtained less than 60 marks?
Answer: 43
(iv) Find the cumulative frequency of the class 50 - 60.
Answer: 43
This page was last modified on
27 January 2026 at 14:32