Part A: Mean = 59.1, Part B: Median = 55, Part C: Mode = 58, Part D: The choice depends on the measure of central tendency suitable for the distribution; if the distribution is skewed, the median may be preferred.
Part A: To find the mean, we sum all the data points and divide by the total number of data points. For this stem-and-leaf plot, the mean is calculated as follows: (35 + 42 + 46 + 51 + 57 + 68 + 54 + 55 + 58 + 58) / 10 = 591 / 10 = 59.1.
Part B: To determine the median, we arrange the data in ascending order and find the middle value. In this case, the ordered data set is {35, 42, 46, 51, 54, 55, 57, 58, 58, 68}, and the median is the average of the two middle values, 54 and 55, which is 54.5.
Part C: The mode is the most frequently occurring value. In this dataset, the number 58 appears twice, making it the mode.
Part D: Comparing the values, the choice of mean, median, or mode depends on the distribution's characteristics. If the data is symmetrically distributed, the mean may be a suitable measure. If the data is skewed, the median might be more representative. In cases where there is a clear mode, it can be a relevant measure. Considering this, one could argue that in this dataset, the median of 54.5 might be a better representation since it is less influenced by outliers and provides insight into the central tendency of the data without being skewed by extreme values.