There are three box plots given for three car series: Box plot one with Q1= 27, Q2 = 33 and Q3 = 41. Box plots two with Q1 = 38, Q2 = 42 and Q3 = 55. And Box plot three with Q1 = 42, Q2 = 46 and Q3 = 57.

Question

There are three box plots given for three car series: Box plot one with Q1= 27, Q2 = 33 and Q3 = 41. Box plots two with Q1 = 38, Q2 = 42 and Q3 = 55. And Box plot three with Q1 = 42, Q2 = 46 and Q3 = 57.
a. In a complete sentences, describe what the shape of each box plot implies about the distribution of the data collected for the car series.
b. Compare the three box plots. What do you imply about the age of purchasing a BMW from the series when compared to each other?

GPT-4o mini · Answer

### a. Shape of Each Box Plot - **Box Plot One**: The first box plot, with Q1 = 27, Q2 = 33, and Q3 = 41, suggests a relatively symmetrical distribution with a moderate spread. However, since the interquartile range (IQR = Q3 - Q1 = 41 - 27 = 14) is not excessively large, it indicates a concentration of data values around the median of 33. The lower Q1 value also suggests some degree of left skewness, indicating possible outliers or lower values present in the dataset. - **Box Plot Two**: In the second box plot, with Q1 = 38, Q2 = 42, and Q3 = 55, the distribution appears to be slightly right-skewed due to the larger IQR of 17. This skewness suggests that while many values are concentrated between 38 and 42, there are higher values leading to a larger Q3, indicating the presence of some older vehicles in the dataset. - **Box Plot Three**: The third box plot, with Q1 = 42, Q2 = 46, and Q3 = 57, shows a more pronounced right skew as evidenced by the higher spread in the upper quartile. The difference between the median and the upper quartile implies a better representation of older vehicles and suggests that the age range is more dispersed, possibly due to higher values influencing the data. ### b. Comparison of the Three Box Plots When comparing the box plots, it becomes clear that Box Plot One represents the youngest average age of purchasing a car, while Box Plot Three indicates the oldest average age. Specifically, Box Plot One suggests that car transactions occur at an average age of around 33 with most values clustered below 41. In contrast, Box Plot Two shows a middle-age range, averaging around 42 with values going as high as 55, which suggests a moderate lifespan of vehicles among purchasers. Finally, Box Plot Three indicates an older demographic of buyers, as the lower quartile starts at 42 and the median is higher at 46, with a broader age range stretching up to 57. This analysis implies that consumers purchasing from the BMW series tend to skew older than those purchasing from the other series, with Box Plot Three likely representing a market focused more on longevity and potentially higher value vehicles.