Latika Leekha
Last Activity: 10 Years ago
The mean of 5 observations is 4 and their variance is 2.
Three observations are given to be 4, 5 and 6.
Now let the remaining observations be x and y.
Then by the definition of mean we have,
(4 + 5 + 6 + x + y)/ 5 = 4.
This gives, 15 + x + y = 20.
Hence, x + y = 5. …. (1)
Now variance is 2, which means
[(4-4)2 + (5-4)2 + (6-4)2 + (x-4)2 + (y-4)2] / 5 = 2
Hence 0 + 1 + 4 + (x-4)2 + (y-4)2 = 10.
(x-4)2 + (y-4)2 = 5.
Now, from (1) y = 5-x
Hence we have
(x-4)2 + (5-x-4)2 = 5.
This yields
x2 + 16 – 8x + 1 + x2 -2x = 5.
This gives 2x2 -10x +12 = 0
Simplifying this we get
x2 -5x + 6 = 0
(x-2)(x-3) = 0
This gives x = 2, 3.
Hence these are the required two observations.
Thanks & Regards
Latika Leekha
askITIians Faculty
