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Answer :
Final answer:
The range of the data is 97 lbs, given by the smallest and largest extremes. The interquartile range (IQR) is 49 lbs, given as the difference between first quartile (Q1) and third quartile (Q3). The percent of men giving a response in the 151 to 200 pounds range is approximately 25%, as quartiles approximately divide the data into 4 equal parts (each being 25% of the total data set).
Explanation:
To answer your questions about this data set, first let's define a few key terms:
- Range: The difference between the maximum and minimum values in a set of data.
- Interquartile Range (IQR): The range of the middle 50 percent of the data, found by subtracting the first quartile (Q₁) from the third quartile (Q₃).
- Percentiles: Values that divide a rank-ordered set of data into 100 equal parts. For example, the 50th percentile (or median) would be greater than 50 percent of the other observations in the set.
(a) To find the range, you subtract the smallest observation (extreme) from the largest. So, the range of these data is 232 - 135 = 97 lbs.
(b) To find the IQR, you subtract the first quartile from the third quartile. So, the IQR of these data is 200 - 151 = 49 lbs.
(c) We understand that the quartiles divide the data into roughly 4 equal parts, making each part approximately 25% of the total data set. Therefore, the interval from 151 to 200 pounds, being between two quartiles, will contain around 25% of the responses.
Learn more about Data Distribution here:
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