Question

1. a sample of 250 songs from spotify was analyzed using a special algorithm that gives each song a popularity score that is between 0 and 100. although most of the songs in this sample have low popularity scores, a small number of songs have high popularity scores. two measures of center were computed for this sample: 65 and 72. one of these measures is the mean and one is the median. which measure must be the mean? a. the mean must be 65 since the distribution is skewed to the right. b. the mean must be 65 since the distribution is skewed to the left. c. the mean must be 72 since the distribution is skewed to the right. d. the mean must be 72 since the distribution is skewed to the left. e. it’s impossible to answer this question without seeing the actual data set.

Explanation:

Step1: Analyze data skewness

Since most songs have low popularity scores and a small number have high popularity scores, the distribution is skewed to the right.

Step2: Recall property of mean and median in skewed - right distribution

In a right - skewed distribution, the mean is pulled in the direction of the tail (higher values), and the mean is greater than the median.

Step3: Compare given values

Given the two measures of center 65 and 72, since the mean is greater than the median in a right - skewed distribution, the mean must be 72.

Answer:

C. The mean must be 72 since the distribution is skewed to the right.