Q. Calculate the standard deviation of the following data:
Marks | 78-80 | 80-82 | 82-84 | 84-86 | 86-88 | 88-90 |
No. of students | 3 | 15 | 26 | 23 | 9 | 4 |
Answer:
Below table represents the frequency distribution of data required for calculating the standard deviation.
Table: Frequency distribution of data
ClassInterval | Midvalue X | Frequency‘f’ | d = x-832 | Fd | fd^{2} |
78-80 | 79 | 3 | -2 | -6 | 12 |
80-82 | 81 | 15 | -1 | -15 | 15 |
82-84 | 83 | 26 | 0 | 0 | 0 |
84-86 | 85 | 23 | 1 | 23 | 23 |
86-88 | 87 | 9 | 2 | 18 | 36 |
88-90 | 89 | 4 | 3 | 12 | 36 |
80 | 32 | 122 |