Final answer:
The dataset's minimum value is 3, the first quartile (Q1) is 26, the median (second quartile, Q2) is 40, the third quartile (Q3) is 71, the maximum value is 139, and the interquartile range (IQR) is 45.
Step-by-step explanation:
To calculate the given statistical values for the dataset (3, 25, 26, 29, 38, 42, 56, 71, 74, 139), we follow these steps:
Minimum: The minimum value (also known as the lowest value) is the smallest number in the dataset. For the given dataset, the minimum value is 3.
Q1 (First Quartile): To find the first quartile, you take the median of the first half of the data (when arranged in ascending order). There are 5 numbers in the first half: 3, 25, 26, 29, 38. The median of these is 26, so the first quartile is 26.
Median: The median is the middle value when you arrange the data in order. With 10 data points, the median will be the average of the 5th and 6th values: (38 + 42) / 2 = 40.
Q3 (Third Quartile): Similarly, to find the third quartile, we take the median of the second half of the data. For the last 5 numbers: 42, 56, 71, 74, 139, the median is 71, so the third quartile is 71.
Maximum: The maximum value is the highest value in the dataset, which is 139 for this set.
Interquartile Range (IQR): The IQR is the difference between the third and first quartiles. So, IQR = Q3 - Q1 = 71 - 26 = 45.