Question

fisherman a and fisherman b each recorded the weights of all the fish they caught, and each created a histogram representing the distribution of weights. the median weight of the fish for both fishermen is equal. however, for fisherman a the mean weight is less than the median, and for fisherman b the mean weight is greater than the median. which statement is most likely correct?
a. fisherman as histogram is skewed left because the weights of his fish include outliers that are greater than the median weight.
b. fisherman bs histogram is skewed left because the weights of his fish include outliers that are less than the median weight.
c. fisherman as histogram is skewed right because the weights of his fish include outliers that are less than the median weight.
d. fisherman bs histogram is skewed right because the weights of his fish include outliers that are greater than the median weight.

Explanation:

Step1: Recall skewness and outlier - median relationship

In a right - skewed distribution, the mean is greater than the median and there are large outliers pulling the mean upwards. In a left - skewed distribution, the mean is less than the median and there are small outliers pulling the mean downwards.

Step2: Analyze Fisherman A

For Fisherman A, the mean weight is less than the median. This implies that there are small outliers (values less than the median) pulling the mean downwards. A distribution with small outliers pulling the mean downwards is left - skewed.

Step3: Analyze Fisherman B

For Fisherman B, the mean weight is greater than the median. This implies that there are large outliers (values greater than the median) pulling the mean upwards. A distribution with large outliers pulling the mean upwards is right - skewed.

Answer:

D. Fisherman B's histogram is skewed right because the weights of his fish include outliers that are greater than the median weight.