Question :
| Expenditure (in Rs) | 1000 – 1500 | 1500 – 2000 | 2000 – 2500 | 2500 – 3000 | 3000 – 3500 | 3500 – 4000 | 4000 – 4500 | 4500 – 5000 |
| Manual workers (frequency) | 24 | 40 | 33 | 28 | 30 | 22 | 16 | 7 |
Solution :
The class (1500 – 2000) has maximum frequency i.e. 40, therefore this is the modal class.
Lower limit of the modal class = l = 1500
Class interval h = 500
Frequency of the modal class = \(f_k\) = 40
Frequency of the class preceding the modal class = \(f_{k – 1}\) = 24
Frequency of the class succeeding the modal class = \(f_{k + 1}\) = 33
We know that,
Mode = l + h(\(f_k – f_{k-1}\over 2f_k – f_{k-1} – f_{k+1}\))
= 1500 + 500(\(40 – 24\over 2(40) – 24 – 33\))
= 1500 + 500(\(16\over 23\))
= 1500 + 347.83
= 1847.83
Hence, the average expenditure done by the maximum number of manual workers is 1847.83.
