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प्रश्न
The mean of 6 numbers is 42. If one number is excluded, the mean of the remaining number is 45. Find the excluded number.
उत्तर
Let `barx` be the mean of n number of observation x1, x2, x3, ..., xn
Mean of given data = `(x_1 + x_2 + x_3 + ... + x_n)/ (n)`
Given that mean of 6 number is 42.
That is,
`(x_1 + x_2 + x_3 + ... + x_6)/ (6) = 42`
⇒ x1 + x2 + x3 + ... + x6 = 6 x 42
⇒ x1 + x2 + x3 + x4 + x5 = 252 - x6 ...( 1 )
Also, given that the mean of 5 number is 45.
That is,
` ( x_1 + x_2 + x_3 + x_4 + x_5)/( 5 ) = 45`
⇒ x1 + x2 + x3 + x4 + x5 = 5 x 45
⇒ x1 + x2 + x3 + x4 + x5 = 225 ....( 2 )
From equation ( 1 ) and ( 2 ), we have
x1 + x2 + x3 + x4 + x5 = 252 - x6 = x1 + x2 +x3 + x4 + x5 = 225
252 - x6 = 225
⇒ x6 = 252 - 225 = 27
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