Question

damon recorded the snowfall in his town for each day of january. this line plot shows the distribution. snowfall in january complete the sentences. the distribution of snowfall amounts is best described as not symmetric. so, the median is a more appropriate measure of variation than the ______. mean median standard deviation interquartile range

Explanation:

Step1: Analyze the distribution

The line plot shows a skewed (not symmetric) distribution. For skewed distributions, the median is a better measure of center, and the interquartile range (IQR) is a better measure of variation than the standard deviation (which is used with mean for symmetric distributions). The mean is affected by skewness, so we need a measure of variation that pairs with median. The interquartile range is used with median for skewed data.

Step2: Determine the appropriate measure

Since the distribution is not symmetric (skewed), the median is the center measure, and the interquartile range is the appropriate measure of variation (as it's resistant to skewness), while standard deviation is paired with mean (sensitive to skewness). The blank is for the measure that's less appropriate, but wait, the sentence is "the median is a more appropriate measure of variation than the ___"? Wait, no, median is a measure of center, not variation. Wait, maybe a typo. Wait, the first blank (after "the"): maybe it's a measure of variation. Wait, the options are mean, median, standard deviation, interquartile range. Wait, the sentence: "the [blank] is a more appropriate measure of variation than the [blank]". Wait, no, median is a measure of center. Wait, maybe the first dropdown was "median" (measure of center), and the second is for measure of variation. Wait, the options for the blank (the one with the line) are mean, median, standard deviation, interquartile range. Wait, the distribution is not symmetric, so for measure of variation, interquartile range (IQR) is better than standard deviation (since standard deviation is affected by skewness, IQR is resistant). But the sentence is "the median is a more appropriate measure of variation than the ___"? No, median is not a measure of variation. Wait, maybe a mistake in the problem, but looking at the options, the last part: "is a more appropriate measure of variation than the ___". Wait, the first part: "the [measure] is a more appropriate measure of variation...". Wait, median is a measure of center, so maybe the first dropdown was supposed to be a measure of variation. Wait, no, the user's problem: the sentence is "The distribution of snowfall amounts is best described as not symmetric. So, the median is a more appropriate measure of variation than the ___". Wait, that's incorrect, median is center. But maybe the problem has a typo, and the first blank (before "is") is a measure of variation. But given the options, the correct pair: for skewed data, median (center) and interquartile range (variation) are better than mean and standard deviation. But the sentence structure: "the [blank] is a more appropriate measure of variation than the ___". Wait, maybe the first blank was supposed to be "interquartile range" and the second "standard deviation", but the first dropdown was "median" (maybe a mistake). But looking at the options, the blank (the one to fill) is among mean, median, standard deviation, interquartile range. Wait, the sentence: "the median is a more appropriate measure of variation than the ___" – no, median is not a measure of variation. So maybe the first dropdown was a measure of variation, like "interquartile range", and the second is "standard deviation". But the user's problem: the first dropdown is "median" (selected), and the blank is below. Wait, the options for the blank are mean, median, standard deviation, interquartile range. Wait, the correct answer: since the distribution is not symmetric (skewed), the mean is affected by skewness, and standard deviation (which depends on mean) is also affected. The interquartile range (IQR) is a measure of variation that's resistant to skewness, paired with median (center). But the sentence is "the median is a more appropriate measure of variation than the ___" – that's wrong, median is center. So maybe the problem meant "the interquartile range is a more appropriate measure of variation than the standard deviation", but the first dropdown was "median" (measure of center). Alternatively, maybe the question has an error, but looking at the options, the correct answer for the blank (the one to fill) is "standard deviation", but no. Wait, the sentence: "the median is a more appropriate measure of variation than the ___" – no, median is not variation. So maybe the first part was "the interquartile range" instead of "the median". But given the options, the only measure of variation among the options is standard deviation and interquartile range. Median and mean are measures of center. So the sentence is incorrect, but assuming that it's a mistake and the intended is that for skewed data, the interquartile range (variation) is better than standard deviation, but the first part is "median" (center). Alternatively, the blank is "standard deviation", because median (center) is better than mean (center) for skewed data, but the question says "measure of variation", which is wrong. But given the options, the most probable answer is "standard deviation", because mean is center, median is center, standard deviation is variation (paired with mean), interquartile range is variation (paired with median). So the sentence is wrong, but the blank should be "standard deviation", because median (center) is better than mean (center), but the question says "measure of variation", which is incorrect. But maybe the problem meant "measure of center", but the options for variation. Alternatively, the answer is "standard deviation", because for skewed data, standard deviation (variation) is less appropriate than interquartile range, but the sentence says "the median is a more appropriate measure of variation than the ___" – no. I think there's a mistake in the problem, but based on the options, the correct answer for the blank (the one to fill) is "standard deviation", because median (center) is better than mean (center), but the question's wording is wrong. Wait, no, the options are mean, median, standard deviation, interquartile range. The sentence: "the median is a more appropriate measure of variation than the ___" – median is not variation, so maybe the first part was "interquartile range" (variation) and the second "standard deviation". But the first dropdown is "median" (center). Given the confusion, but the key is: for skewed (not symmetric) data, median (center) and interquartile range (variation) are better than mean and standard deviation. So the blank (the one to fill) should be "standard deviation", because the sentence is trying to say that a measure (maybe interquartile range, but it's median) is better than standard deviation for variation. But I think the intended answer is "standard deviation".

Answer:

standard deviation