The weights of tea in 70 packets are shown in the following table:
Weight (in grams) | 200 - 201 | 201 - 202 | 202 - 203 | 203 - 204 | 204 - 205 | 205 - 206 |
Number of packets | 13 | 27 | 18 | 10 | 1 | 1 |
Find the mean weight of packets using step - deviation method.
We will find the mean weight of packet using step - deviation method, where A = Assumed mean and h = length of class interval.
Here, let A = 202.5 and h = 1
WEIGHT(g) | MID - POINT(xi) | DEVIATION(di) di = xi – 202.5 | NUMBER OF PACKETS(fi) | ui = di/h | fiui |
200 - 201 | 200.5 | - 2 | 13 | - 2 | - 26 |
201 - 202 | 201.5 | - 1 | 27 | - 1 | - 27 |
202 - 203 | 202.5 = A | 0 | 18 | 0 | 0 |
203 - 204 | 203.5 | 1 | 10 | 1 | 10 |
204 - 205 | 204.5 | 2 | 1 | 2 | 2 |
205 - 206 | 205.5 | 3 | 1 | 3 | 3 |
TOTAL | 70 | - 38 |
We have got
A = 202.5, h = 1, Σfi = 70 & Σfiui = - 38
∵ mean is given by
⇒ 
⇒ 
Thus, mean is 201.96 g.
21