Weight? Wait what? Marcos asked a random sample of $50$mall shoppers for their weight. Twenty-five of the shoppers were asked directly and the other $25$ were asked anonymously by means of a “secret ballot.” The mean reported weight was$13$ pounds heavier for the anonymous group. Explain why the two means are so different.

We have to explain why the two means are so different.

Marcos inquired about the weight of a random sample of $50$mall patrons. Two of the groups were split in half. The first half of the group was asked directly about their weight, while the other half was asked anonymously through "secret ballot." As a result, the anonymous group's mean was greater than the group that was personally questioned. This is because, for personal reasons, people do not want to confess their true weight when they are questioned directly. They don't want other people to know how much they weight.

As a result, when they were asked directly, the survey results were skewed since their responses were fake. When they were asked about their weight anonymously, they knew their identity would be kept hidden, so they gave honest answers in the survey. As a result, they are distinct.