Answer to Question #298371 in Statistics and Probability for ashiney

Question #298371

An analysis of the monthly allowances received by a sample of five engineers from a telco company has been conducted recently. The mean and median of the allowances is RM7000. A unimodal among the observations is RM12,000. Find the standard deviation if the allowances paid to each engineer were in full thousands. 


1
Expert's answer
2022-02-17T04:06:10-0500

Solution:

Mean=7000

Median=7000

Mode (one)=12000

n=5

Assume two unknown values are x and y.

Arranging in ascending order,

x, y, 7000, 12000, 12000

Mean = 7000

x+y+7000+12000+120005=7000x+y=4000 ...(i)\dfrac{x+y+7000+12000+12000}5=7000 \\ \Rightarrow x+y=4000\ ...(i)

Also, xyx\ne y as there is unimode...(ii)

Also, x, y are in thousands...(iii)

From (i), (ii), (iii)

x=1000,y=3000x=1000,y=3000

Now, standard deviation=1n1Σ(xixˉ)2=\sqrt{\dfrac1{n-1}\Sigma(x_i-\bar x)^2}

=151[(10007000)2+(30007000)2+(70007000)2+(120007000)2+(120007000)2=\sqrt{\dfrac1{5-1}[(1000-7000)^2+(3000-7000)^2+(7000-7000)^2+(12000-7000)^2+(12000-7000)^2}

=5049.752469=5049.752469


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