which measure of variation is most sensitive to extreme values? choose the correct answer below. histogram median range mean

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# Brief Explanations:
- A histogram is a graphical representation, not a measure of variation, so it's eliminated.
- The median is a measure of central tendency (middle value) and is resistant to extreme values.
- The mean is also a measure of central tendency, and it is sensitive to extreme values as it's calculated using all data points (including outliers).
- The range is a measure of variation (difference between max and min) and is sensitive to extreme values, but among the options, the mean is a measure of central tendency that's highly sensitive. Wait, no—wait, the question is about measure of variation. Wait, range is a measure of variation. Wait, let's re - evaluate:
    - Histogram: Not a measure (it's a graph), so out.
    - Median: Measure of central tendency, not variation, and resistant to extremes.
    - Mean: Measure of central tendency, sensitive to extremes, but the question is about measure of variation. Wait, the options might have a mix. Wait, the question is "which measure of variation...", but mean is central tendency. Wait, maybe a mis - option? Wait, no—wait, range is a measure of variation. But mean is a central tendency measure. Wait, perhaps the question has a typo, but among the options:
        - Histogram: Not a measure.
        - Median: Central tendency, resistant.
        - Mean: Central tendency, sensitive to extremes.
        - Range: Measure of variation, sensitive to extremes (since it's max - min, an extreme max or min affects it). But if we consider the options, maybe the intended answer is Range? Wait, no—wait, the mean is a measure of central tendency, but maybe the question is mis - phrased. Wait, let's check definitions:
            - Measure of variation: range, variance, standard deviation, etc.
            - Measure of central tendency: mean, median, mode.
            - Histogram: graphical display.

So among the options, the only measure of variation is Range. But wait, the mean is sensitive to extremes (central tendency), but the question is about measure of variation. So the correct answer should be Range? Wait, no—wait, maybe the question is wrong, but let's go by the options. Wait, the options are Histogram (not a measure), Median (central tendency, resistant), Mean (central tendency, sensitive), Range (measure of variation, sensitive). So if we strictly follow "measure of variation", then Range. But if we consider the sensitivity to extremes, mean is very sensitive, but it's a central tendency measure. Maybe the question has a mistake, but among the options, the answer is Range? Wait, no—wait, let's think again. The range is calculated as maximum value minus minimum value. An extreme value (either very large or very small) will directly affect the range. The mean is affected by extreme values but it's a measure of central tendency. So if the question is about measure of variation, the answer is Range. But if it's about measure (including central tendency) sensitive to extremes, mean. But the question says "measure of variation". So the correct option is Range? Wait, no—wait, maybe the question is mis - worded. Let's check the options again. The options are Histogram, Median, Range, Mean.

So:

- Histogram: Not a measure, so eliminate.
            - Median: Measure of central tendency, resistant to extremes (since it's the middle value, outliers don't affect it much).
            - Range: Measure of variation, calculated as max - min. An extreme value (high or low) will change the max or min, thus changing the range. So it's sensitive to extreme values.
            - Mean: Measure of central tendency, calculated as sum of all values divided by number of values. An extreme value (high or low) will change the sum, thus changing the mean. So it's sensitive to extreme values, but it's a measure of central tendency, not variation.

Since the question asks for a measure of variation, the answer is Range. But if we ignore the "measure of variation" and just look for the one sensitive to extremes among the options, mean is also sensitive, but it's a central tendency measure. Given the options, the intended answer is likely Range? Wait, no—wait, maybe the question is wrong, but let's go with the options. The correct answer is Range? Wait, no—wait, let's check a reference. The range is a measure of variation and is sensitive to extreme values because it only depends on the maximum and minimum values. The mean is a measure of central tendency and is also sensitive to extreme values. But the question specifies "measure of variation", so among the options, Range is the measure of variation that is sensitive to extreme values.

# Answer:
Range (the option labeled "Range")

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