Question

(a) complete the grouped frequency distribution for the data. (note that the class width is 6.)
test scores frequency
66 to 71 4
72 to 77 4
78 to 83 2
84 to 89

Explanation:

Step1: Assume total number of data points is not given, but we can use the fact that the frequency distribution should account for all data. However, without more information, if we assume this is a complete set of intervals and we want to find the missing frequency in a normal - distribution - like scenario (not given explicitly), we note that we have no other way to calculate the frequency other than by some external knowledge about the data. Since no other data is provided, we assume the data is evenly distributed in a sense of the pattern shown so far. But this is a weak assumption. In the absence of more data, we can't accurately calculate the frequency. If we assume that the data follows a certain pattern and we have no reason to believe otherwise, we might consider that the frequencies seem to be somewhat consistent so far.

Let's assume we have no other information and we want to make a simple guess. Since the first two intervals have frequency 4 and the third has frequency 2, we might assume the fourth has frequency 2 to follow a loose pattern.

Answer:

2