The table given below are the yields of 4 varieties in a 4 replicate experiment in which one observation is missing. Analyze the data after finding missing value

A 12 C 19 B 10 D 10
C 17 B 13 D 7 A ?
B 21 D 11 A 6 C 19
D 12 A 7 C 27 B 18

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Solution:

Let x be the missing observation.

Treatment Block
I II III IV
A 12 x 6 7
B 10 13 21 18
C 19 17 19 27
D 10 7 11 12

Here,

Number of blocks (r) = 4

Number of column (C) = 4

Number of Treatment (k) = 4

Sum of remaining values in the block with missing observation(b) = 13 + 17 + 7 = 37

Sum of remaining values of the treatment and with the missing observation(T) = 12 + 6 + 7 = 25

Grand Total (G) = 209

Now,

\(x = \frac{rB + KT – G}{(r-1)(C-1)}\)

\(= \frac{4 \times 37 + 4 \times 25 – 209}{(4-1)(4-1)}\)

= 4.33

Therefore, the missing observation is 4.33

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