Final answer:
Given the range of 63 for a data set of 200 observations, the approximate interquartile range can be estimated by dividing the range by 2, resulting in an IQR of 31.5, which corresponds to option b).
Step-by-step explanation:
The question concerns determining the approximate interquartile range (IQR) given a data set with 200 observations and a range of 63. The interquartile range is the measure of the spread of the middle half of the data, calculated as the difference between the third quartile (Q3) and the first quartile (Q1). Although we do not have the individual quartiles, we can use an approximation method by recognizing that the range is divided approximately evenly among the four quarters of the data.
Since each quarter represents about 25% of the data, we can estimate that the IQR, which spans the middle 50%, is roughly half of the total range. Therefore, to approximate the IQR for the given data set, we would take 63 and divide it by 2, resulting in an IQR of approximately 31.5. This method assumes a relatively uniform distribution across the range, which may not be accurate for all data sets, but it provides an acceptable estimate for the purposes of this question.
In the context of the options provided, the approximate interquartile range of the data set with a range of 63 would therefore be 31.5, which corresponds with option b).