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Question
Find the mean and variance of frequency distribution given below:
| xi: | 1 ≤ x < 3 | 3 ≤ x < 5 | 5 ≤ x < 7 | 7 ≤ x < 10 |
| fi: | 6 | 4 | 5 | 1 |
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Solution
| xi | Mid-Values(yi) | yi2 | fi | fi yi | fi yi2 |
| 1–3 | 2 | 4 | 6 | 12 | 24 |
| 3–5 | 4 | 16 | 4 | 16 | 64 |
| 5–7 | 6 | 36 | 5 | 30 | 180 |
| 7–10 | 8.5 | 72.25 | 1 | 8.5 | 72.25 |
| `sum f_i = 16` |
\[\sum_{} f_i y_i = 66 . 5\]
|
\[\sum_{}$ f_i {y_i}^2 = 340 . 25\]
|
Therefore,
Mean =
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