Which of the following does not change for the observation $23, 50, 27, 2 x, 48, 59, 72, 89, 5 x, 100, 120$ when $x$ lies between $15$ and $20$ ?

Arithmetic mean

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Range

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Median

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Quartile deviation

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Solution

The correct option is D Range
$23, 50, 27, 2 x, 48, 59, 72, 89, 5 x, 100, 120$
Now, when x lies in $15$ and $20$ , the numbers $2 x$ and $5 x$ may range between $30, 75$ and $40, 100$ respectively.
Thus, there will be no effect on the minimum value and maximum value. Hence, the range of the series will not be affected.

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