127, 125, 125, 129, 123, 126, 127, 128, 128, 125
Find the range and the interquartile range of the dataset.
The range is $$, and interquartile range is $$.
To find the range, we need to subtract the smallest value from the largest value in the dataset:
Range = 129 - 123 = 6
To find the interquartile range, we first need to find the first quartile (Q1) and the third quartile (Q3) of the dataset.
Step 1: Order the dataset in ascending order:
123, 125, 125, 125, 126, 127, 127, 128, 128, 129
Step 2: Calculate the median to find the first quartile (Q1) and third quartile (Q3):
Q1 = Median of the lower half = Median of 123, 125, 125, 125, 126 = 125
Q3 = Median of the upper half = Median of 127, 127, 128, 128, 129 = 128
Step 3: Calculate the interquartile range (IQR) using the formula:
IQR = Q3 - Q1
IQR = 128 - 125 = 3
Therefore, the range of the dataset is 6 and the interquartile range is 3.