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Question
The following table gives the number of pages written by Sarika for completing her own book for 30 days:
| Number of pages written per day |
16 – 18 | 19 – 21 | 22 – 24 | 25 – 27 | 28 – 30 |
| Number of days | 1 | 3 | 4 | 9 | 13 |
Find the mean number of pages written per day.
Solution
No need to change the class-intervals into continuous intervals as Classmarks of continuous and discontinuous classes are same.
di is deviation from assumed mean.
| Class interval | Mid Value `(bb(x_i))` |
`bb(d_i = (x_i - a))` | No. of days `(bb(f_i))` |
`bb(f_i d_i)` |
| 16 – 18 | 17 | – 6 | 1 | – 6 |
| 19 – 21 | 20 | – 3 | 3 | – 9 |
| 22 – 24 | a = 23 | 0 | 4 | 0 |
| 25 – 27 | 26 | 3 | 9 | 27 |
| 28 – 30 | 29 | 6 | 13 | 78 |
| `sumf_i = 30` | `sumf_i d_i = 90` |
a = assumed mean, a = 23
`barx = a + (sumf_i d_i)/(sumf_i)`
= `23 + 90/30`
= 23 + 3
= 26
∴ `barx` = 26
Hence, the mean of pages written per day is 26.
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