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(C) The arithmetic mean is calculated by summing all the observations and dividing by the total number of observations. Because it incorporates the va

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Arithmetic mean

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(C) The arithmetic mean is calculated by summing all the observations and dividing by the total number of observations. Because it incorporates the value of every single data point,the inclusion of an extreme value (an outlier) significantly shifts the sum,thereby changing the mean. In contrast,the median and mode are positional or frequency-based measures that are much more robust against extreme values. Therefore,the arithmetic mean is the most affected by extreme observations.

$x_i$	$3$	$6$	$10$	$12$	$7$	$15$
$f_i$	$3$	$4$	$2$	$8$	$13$	$10$

Which of the following averages is most affected by extreme observations?

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