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Question Number 176098 by nadovic last updated on 12/Sep/22

The deviations of a set of numbers from 12 are 3, −2, 1, 0, −1, 4, 0, 1 and 2. Calculate the mean and standard deviation of the numbers.

$$\mathrm{The}\:\mathrm{deviations}\:\mathrm{of}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{numbers} \\ $$$$\mathrm{from}\:\mathrm{12}\:\mathrm{are}\: \\ $$$$\:\:\:\:\:\mathrm{3},\:−\mathrm{2},\:\mathrm{1},\:\mathrm{0},\:−\mathrm{1},\:\mathrm{4},\:\mathrm{0},\:\mathrm{1}\:\mathrm{and}\:\mathrm{2}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{standard}\: \\ $$$$\mathrm{deviation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}. \\ $$

Answered by Rasheed.Sindhi last updated on 12/Sep/22

(12−a_1 )+(12−a_2 )+(12−a_3 )+...+(12−a_9 ) = 3+(−2)+1+ 0+(−1)+ 4+ 0+1+2=8 12×9−(a_1 +a_2 +...+a_9 )=8 a_1 +a_2 +...+a_9 =108−8=100 mean=((a_1 +a_2 +...+a_9 )/9)=((100)/9)

$$\left(\mathrm{12}−{a}_{\mathrm{1}} \right)+\left(\mathrm{12}−{a}_{\mathrm{2}} \right)+\left(\mathrm{12}−{a}_{\mathrm{3}} \right)+...+\left(\mathrm{12}−{a}_{\mathrm{9}} \right) \\ $$$$\:\:\:\:\:=\:\mathrm{3}+\left(−\mathrm{2}\right)+\mathrm{1}+\:\mathrm{0}+\left(−\mathrm{1}\right)+\:\mathrm{4}+\:\mathrm{0}+\mathrm{1}+\mathrm{2}=\mathrm{8} \\ $$$$\mathrm{12}×\mathrm{9}−\left({a}_{\mathrm{1}} +{a}_{\mathrm{2}} +...+{a}_{\mathrm{9}} \right)=\mathrm{8} \\ $$$${a}_{\mathrm{1}} +{a}_{\mathrm{2}} +...+{a}_{\mathrm{9}} =\mathrm{108}−\mathrm{8}=\mathrm{100} \\ $$$${mean}=\frac{{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +...+{a}_{\mathrm{9}} }{\mathrm{9}}=\frac{\mathrm{100}}{\mathrm{9}} \\ $$

Commented by peter frank last updated on 12/Sep/22

thanks

$$\mathrm{thanks} \\ $$

Commented by Rasheed.Sindhi last updated on 12/Sep/22

thanks for thanks!

$$\mathrm{thanks}\:\mathrm{for}\:\mathrm{thanks}! \\ $$

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