QQuestion
The following table gives the duration of movies in minutes:
| Duration (minutes) | Number of movies |
|---|---|
| 100–110 | 5 |
| 110–120 | 10 |
| 120–130 | 17 |
| 130–140 | 8 |
| 140–150 | 6 |
| 150–160 | 4 |
Using the step-deviation method, find the mean duration of the movies.
✓Answer
Class width, i = 10. Take the assumed mean A = 135.
| Class | Class mark x | d = x − A | u = d/i | 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 | 135 | 0 | 0 | 8 | 0 |
| 140–150 | 145 | 10 | 1 | 6 | 6 |
| 150–160 | 155 | 20 | 2 | 4 | 8 |
Σf = 50 and Σfu = −38
Mean = A + \frac{\Sigma fu}{\Sigma f}\times i
⇒ Mean = 135 + \frac{-38}{50}\times10
⇒ Mean = 135 − 7.6
⇒ Mean = 127.4 minutes
Therefore, the mean duration is 127.4 minutes.
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