Final answer:
The interquartile range (IQR) for the provided dataset is calculated by finding the first and third quartiles (Q1 and Q3) and taking their difference. The IQR for this data set is 59.
Step-by-step explanation:
The interquartile range (IQR) is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). To find the IQR, we first need to determine Q1 and Q3 by dividing the data set into four equal parts.
The interquartile range (IQR) is the range of the middle 50 percent of the data values.
To find the IQR, we need to calculate the first quartile (Q1) and the third quartile (Q3). To do this, we need to order the data set in ascending order. In this case, the ordered data set would be: 101, 101, 127, 134, 155, 160, 177, 189, 190, 190.
Q1 can be calculated as the median of the lower half of the data set, which is the 5th value (155). Q3 can be calculated as the median of the upper half of the data set, which is the 6th value (177).
Therefore, Q1 = 155 and Q3 = 177.Since there are 10 data points in the question's dataset, Q1 is the average of the 2.5th and 3rd data point, and Q3 is the average of the 7.5th and 8th data point.
Sorting the data: 101, 101, 127, 134, 155, 160, 177, 189, 190, 190
Q1 (First Quartile) = (127+134)/2 = 130.5
Q3 (Third Quartile) = (189+190)/2 = 189.5
Now, the IQR is calculated as:
IQR = Q3 - Q1 = 189.5 - 130.5 = 59
The interquartile range for this set of data is 59.