Question

consider a distribution of the weights of 100 eighth-grade boys. how many modes would you expect for the distribution? would you expect the distribution to be symmetric, left-skewed, or right-skewed?

Answer 1

Since we are considering all 100 8th grade boys we would expect maximum number of people to have weights which are in the similar range. Now mode is the value which has the highest frequency. So here we would expect one mode only.

There could be a few outliers in the data, say a few overweight or underweight students because of different eating habits and different metabolism rates but we wouldn't expect many outliers.

Since the students are all 8th graders, we would expect the maximum number of people with similar weights and hence expect the mean weight to be equal to the median to be equal to the mode. So we would expect the distribution to be symmetrical.