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Question
Using an appropriate method, find the mean of the following frequency distribution:
| Class | 84-90 | 90-96 | 96-102 | 102-108 | 108-114 | 114-120 |
| Frequency | 8 | 10 | 16 | 23 | 12 | 11 |
Which method did you use, and why?
Solution
| Class | Frequency `(f_i)` | Mid values `(x_i)` | `(f_i x_i)` |
| 84-90 | 8 | 87 | 696 |
| 90-96 | 10 | 93 | 930 |
| 96-102 | 16 | 99 | 1584 |
| 102-108 | 23 | 105 | 2415 |
| 108-114 | 12 | 111 | 1332 |
| 114-120 | 11 | 117 | 1287 |
| Total | `∑f_i` = 80 |
`∑ f_i x_i = 8244` |
The mean of the data is given by,
x =` (sum_(i) f_i x_i)/(sum _(i) f_i)`
=`8244/80`
=103.05
Thus, the mean of the following data is 103.05.
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