Question

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.

Answer 1

Let us choose a = 202.5, h = 1, then `d_i = x_i - 202.5 and u_i = (x_i-202.5)/1`

Using step-deviation method, the given data is shown as follows:

Weight (in grams)	Number of packets `(f_i)`	Class mark `(x_i)`	`d_i = x_i - 202.5`	`u_i = (x_i−202.5)/ 1`	`(f_i u_i)`
200 – 201	13	200.5	-2	-2	-26
201 – 202	27	201.5	-1	-1	-27
202 – 203	18	202.5	0	0	0
203 – 204	10	203.5	1	1	10
204 – 205	1	204.5	2	2	2
205 – 206	1	205.5	3	3	3
Total	`Ʃ f_i` = 70				`Ʃ f_i u_i` = -38

The mean of the given data is given by, 

x = `a + ((sumf_i u_i)/( sumf_i)) xx h`

    = `202.5 + ((-38)/70) xx1`

    = 202.5 – 0.542
    = 201.96
Hence, the mean is 201.96 g.