Question -
Answer -
| Daily wages (in Rs.) | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |
| Number of workers | 12 | 14 | 8 | 6 | 10 |
Find the mean daily wages of the workers of the factory by using anappropriate method.
Solution:
Find the midpoint ofthe given interval using the formula.
Midpoint (xi) = (upper limit + lower limit)/2
In this case, thevalue of mid-point (xi) is very large, so let us assume the meanvalue, A = 150 and class interval is h = 20.
So, ui = (xi – A)/h = ui = (xi – 150)/20
Substitute and findthe values as follows:
| Daily wages (Class interval) | Number of workers frequency (fi) | Mid-point (xi) | ui = (xi – 150)/20 | fiui |
| 100-120 | 12 | 110 | -2 | -24 |
| 120-140 | 14 | 130 | -1 | -14 |
| 140-160 | 8 | 150 | 0 | 0 |
| 160-180 | 6 | 170 | 1 | 6 |
| 180-200 | 10 | 190 | 2 | 20 |
| Total | Sum fi = 50 | | | Sum fiui = -12 |
So, the formula tofind out the mean is:
Mean = x̄ = A + h∑fiui /∑fi =150+ (20 × -12/50) = 150 – 4.8 = 145.20
Thus, mean daily wageof the workers = Rs. 145.20