Which one of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?

Answer:- 1

Explanation:-

Solution:

The average of the elements in the original set S is:

\begin{aligned} \frac{0 + 2 + 4 + 5 + 9}{5} \\ = \frac{20}{5} \\ = 4 \end{aligned}

$\eqalign{ & \frac{{0 + 2 + 4 + 5 + 9}}{5} \cr & = \frac{{20}}{5} \cr & = 4 \cr}$
If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,

\begin{aligned} \frac{0 + 2 + 5 + 9}{4} \\ = \frac{16}{4} \\ = 4 \end{aligned}

$\eqalign{ & \frac{{0 + 2 + 5 + 9}}{4} \cr & = \frac{{16}}{4} \cr & = 4 \cr}$

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If we remove an element that equals the average, then the average of the new set will remain unchanged. The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is,

\begin{aligned} \frac{0 + 2 + 5 + 9}{4} \\ = \frac{16}{4} \\ = 4 \end{aligned}

$\eqalign{ & \frac{{0 + 2 + 5 + 9}}{4} \cr & = \frac{{16}}{4} \cr & = 4 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

The average of the elements in the original set S is: