Problem 1
The median weight of the Welsh corgis is 27 pounds. This is found in the table in row 1, column 2. Recall that the median is the middle most value, so that means 50% of the Welsh corgi weights will be less than 27 pounds, and also 50% of the weights are greater than 27 pounds.
========================================================
Problem 2
The Welsh corgis have the greater variation in weights. Why is this? There are two pieces of evidence:
The first of which is that the range for the first row (7) is larger than the range in the second row (2). The range is the difference between the max and min. The larger the range, the more spread out the data set will be.
The second piece of evidence is that the MAD (mean absolute deviation) for the Welsh corgis is larger compared to the MAD for the cocker spaniels group. The MAD is another way to measure the spread of a data set. Like the range, the larger the MAD gets, the more spread out the data is. It measures how far on average any given value is from the mean. It's similar to the standard deviation and variance, which are also measures of spread.
========================================================
Problem 3
Both dog breeds have the same mean value, and roughly the same median. Both the mean and median are measures of center. Based on just these two pieces of info alone, we could easily conclude that both dog groups have the same distribution more or less. Furthermore, we could conclude that both groups have roughly the same max weight value.
However, we discussed in problem 2 that the first group (Welsh corgi) is more spread out, so it's likely that could heavily imply that the min and max values are further from the center compared to the second group of dogs. Having a larger max would then mean that the corgi group has the largest weight.
In short, the answer is "Welsh corgi" due to this group having a greater spread, and that pushes the max further away from the center.
