A student calculates the geometric mean of 8 values is 10.5. After rechecking it revealed that one value 15 is missing. Find the correct geometric mean?

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Feb 7, 2018

Answer:

# 15^(1/9)*(10.5)^(8/9)#.

Explanation:

Suppose that the #8# observations are #x_1,x_2,...,x_8#, where,

all #x_i > 0#.

Given that, the GM of #{x_i : i=1,2,...,8}# is #10.5#

#:. root(8)(x_1*x_2*...*x_8)=(x_1*x_2*...*x_8)^(1/8)=10.5#

#:. (x_1*x_2*...*x_8)=(10.5)^8.....................................[ast]#.

Now, taking into account of the missing entry #15#, we now have

#9# observations, namely, #{x_i : i=1,2,...,8}uu{15}#.

Hence, the corrected GM will be given by,

#root(9)(15*x_1*x_2*...*x_8)#,

#=(15*x_1*x_2*...*x_8)^(1/9)#,

#=15^(1/9)*(x_1*x_2*...*x_8)^(1/9)#,

#=15^(1/9)*{(10.5)^8)}^(1/9)#,

#=15^(1/9)*(10.5)^(8/9)#.

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