Question

miguel has a booth at the cards, comics, and games convention, where he sells vintage trading cards. this histogram shows the distribution of the number of trading cards he’s sold to each customer so far today.
trading card sales
complete the sentences.
the distribution of the numbers of trading cards sold is best described as not symmetric. so, the ___ is a more appropriate measure of variation than the
number of trading cards sold
number of customers
1-3
4-6
7-9
10-12
13-15
16-18
mean
median
standard deviation

Explanation:

Step1: Analyze Distribution Symmetry

The histogram's shape (not symmetric, likely skewed) means mean is affected by outliers/skew, median is robust.

Step2: Choose Appropriate Measure

For non - symmetric (skewed) distributions, median is a more appropriate measure of center than mean. For variation, since mean is less appropriate, median - related variation measures? Wait, the second blank: when distribution is not symmetric, median is better for center, and for variation, median absolute deviation? But the options given (mean, median, standard deviation). Wait, the first blank: the distribution is not symmetric, so median is more appropriate measure of center (since mean is pulled by skewness). The second blank: standard deviation is based on mean, so median is better for center, and for variation, but the options for the second part (variation than the... ) Wait, the first sentence: "The distribution of the numbers of trading cards sold is best described as not symmetric. So, the [first blank] is a more appropriate measure of [center?] than the [second blank]." Wait, the options for first blank: median, mean? Wait, no: when distribution is not symmetric, median is better than mean as a measure of center. Then for variation, standard deviation is based on mean, so median is better for center, mean is worse. So first blank: median, second blank: mean. Wait, the options: first blank choices (median, mean, standard deviation? No, the options for the first blank (the measure) and second blank (the other measure). Wait, the text: "So, the [blank1] is a more appropriate measure of [center] than the [blank2]." And then "variation than the [blank3]"? Wait, maybe I misread. Let's re - examine:

The first part: "The distribution of the numbers of trading cards sold is best described as not symmetric. So, the [first blank] is a more appropriate measure of [center] than the [second blank]."

In non - symmetric distributions, median is a better measure of central tendency than mean because mean is influenced by skewness (outliers or skewed tails).

Then the second part: "variation than the [blank]". Standard deviation is calculated using the mean ($\text{Standard Deviation}=\sqrt{\frac{\sum(x - \mu)^2}{n}}$, where $\mu$ is the mean). Since mean is not a good measure of center in skewed distributions, the variation measure based on median (like median absolute deviation) is better, but among the options (mean, median, standard deviation), for the variation part, if we are comparing, since mean is not appropriate for center, standard deviation (based on mean) is less appropriate, and median is better for center. Wait, maybe the first blank is "median", the second blank is "mean", and for the variation part, but the question has two blanks? Wait, the original problem:

First blank: measure of center (median vs mean), second blank: the other measure, and then "variation than the..." Wait, maybe the first sentence:

"The distribution of the numbers of trading cards sold is best described as not symmetric. So, the \underline{median} is a more appropriate measure of \underline{center} than the \underline{mean}. And for variation, median absolute deviation is better, but among the options, if we consider the second part: "variation than the \underline{standard deviation}"? No, maybe the first two blanks:

First blank: median, second blank: mean. Because in non - symmetric distributions, median (a resistant measure) is better than mean (a non - resistant measure) for central tendency.

Step3: Confirm with Distribution Properties

Skewed (non - symmetric) distributions: median is robust to skewness, mean is not. So median is more appropriate than mean as a measure of center.

Answer:

First blank: median; Second blank: mean