Final answer:
The minimum value is 0.01, the first quartile is 0.03, the median is 0.04, the third quartile is 0.85, and the maximum value is 0.9. The IQR is 0.82, and percentiles would need to be interpolated.
Step-by-step explanation:
To determine the minimum, maximum, and quartile values for the given dataset, we first arrange the values in ascending order: 0.01, 0.025, 0.03, 0.04, 0.4, 0.85, 0.9. From this ordered list, we can identify the following:
- a. minimum value: 0.01
- b. first quartile (Q1): 0.03
- c. median (Q2 or second quartile): 0.04
- d. third quartile (Q3): 0.85
- e. maximum value: 0.9
The width of the Interquartile Range (IQR) is the difference between the third quartile and the first quartile: IQR = Q3 - Q1 = 0.85 - 0.03 = 0.82.
To find the 37th percentile and 63rd percentile, we would calculate the positions within the ordered dataset that correspond to 37% and 63% of the way through the data, but as this data set is small, these would be approximated by interpolation or identified as closest to a particular data point.