Answer:
To compare Bob and Alan's points per game, we can use the following summary statistics:
Mean: This is the average of the data set. It can be calculated by adding up all the values and dividing by the number of values.
Median: This is the middle value of the data set when it is arranged in order.
Range: This is the difference between the largest and smallest value in the data set.
Interquartile range (IQR): This is the range of the middle 50% of the data set, calculated as the difference between the 75th and 25th percentiles.
Mean absolute deviation (MAD): This is the average of the absolute differences between each value and the mean.
To compare the center of each player's data, the best measure of central tendency would be the mean. This is because it takes into account all the values in the data set and gives an overall average. The median can also be used, but it only considers the middle value and may not accurately represent the center if there are outliers in the data set.
To compare the spread of each player's data, the best measure of spread would be the range or IQR. This is because they give an idea of the range of values in the data set and how spread out the data is. The MAD can also be used, but it is a more complex calculation and may not provide as clear of an understanding of the spread of the data.
Based on the representations, summary statistics, and interpretations, it is not possible to determine if either friend is a basketball star without more context. A basketball star could have a high average points per game, a narrow range, and a small spread, but this would depend on the level of competition and the type of game being played. A player who consistently scores a high number of points and performs well under pressure could be considered a basketball star, but this cannot be determined solely based on the data presented.