Final answer:
Without the actual data, direct calculation of the frequency distribution table and the mean, mode, median, and range is not possible. However, Option B seems like the most sensible option based on a typical distribution of heights.
Step-by-step explanation:
To address the student's question regarding the construction of a frequency distribution table and the calculation of various statistical measures, we should start by organizing the data into a frequency distribution table with predetermined intervals and then calculate the mean, mode, median, and range of the data.
a) The mean (average) height can be calculated by summing all the height measurements and dividing by the number of girls, which is 20 in this case.
b) The mode is the height value that appears most frequently in the data set.
c) The median is the middle value when the data set is ordered from lowest to highest. If there is an even number of data points, the median is the average of the two middle values.
d) The range is the difference between the maximum and minimum values in the data set.
Without the raw data, we can't compute these values directly, but we can see that Option B (158, 164, 170) aligns with a logical progression of mean, mode, and median for a typical frequency distribution of heights.