4(ii)
The following table gives the duration of movies in minutes.
| Duration (in minutes) | No. of movies |
|---|---|
| 100-110 | 5 |
| 110-120 | 10 |
| 120-130 | 17 |
| 130-140 | 8 |
| 140-150 | 6 |
| 150-160 | 4 |
Using step–deviation method, find the mean duration of the movies.
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In the given table i is the class interval which is equal to 10.
| Class | Class mark (x) | d = (x - A) | u = d/i | Frequency (f) | fu |
|---|---|---|---|---|---|
| 100-110 | 105 | -30 | -3 | 5 | -15 |
| 110-120 | 115 | -20 | -2 | 10 | -20 |
| 120-130 | 125 | -10 | -1 | 17 | -17 |
| 130-140 | A = 135 | 0 | 0 | 8 | 0 |
| 140-150 | 145 | 10 | 1 | 6 | 6 |
| 150-160 | 155 | 20 | 2 | 4 | 8 |
| Total | Σf = 50 | Σfu = -38 |
Mean = A + $\frac{Σfu}{Σf} \times i = 135 + \frac{-38}{50} \times 10$
= $135 + \frac{-380}{50}$
= 135 - 7.6
= 127.4
Hence, mean = 127.4