Question

question 9
2 pts
a sample of college students was surveyed and asked about the amount of money they spend each week on coffee. in this particular sample, most students spend a lot on coffee per week, but a small number of students spend little on coffee. two measures of center were computed for this sample: $19.82 and $21.65. one of these measures is the mean and one is the median. which measure must be the mean?
the mean is $21.65 because the distribution is skewed to the right.
the mean is $21.65 because the distribution is skewed to the left.
the mean is $19.82 because the distribution is skewed to the left.
there is not enough information given in this problem to determine which measure is the mean.
the mean is $19.82 because the distribution is skewed to the right.

Explanation:

Step1: Understand skewness effect

In a right - skewed distribution, the mean is pulled in the direction of the tail (towards the larger values) and is greater than the median. In a left - skewed distribution, the mean is pulled towards the smaller values and is less than the median.

Step2: Analyze the sample

Most students spend a lot on coffee per week, but a small number of students spend little on coffee. This indicates a right - skewed distribution since the small number of students spending little on coffee create a long left - tail.

Step3: Compare mean and median

Since in a right - skewed distribution mean > median, and we have two values $19.82$ and $21.65$, the larger value ($21.65$) must be the mean.

Answer:

The mean is $21.65$ because the distribution is skewed to the right.