The highest temperatures measured at Death Valley, California, from 1995 to 2004 are given as a dataset. 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 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).
To find Q1, we need to find the median of the first half of the dataset. Since the dataset has an even number of values (10), the median will be the average of the two middle values in the first half of the sorted dataset:
123, 125, 125, 125, 126
Median = (125 + 125) / 2 = 125
Q1 = 125
To find Q3, we need to find the median of the second half of the dataset. Again, because the dataset has an even number of values (10), the median will be the average of the two middle values in the second half of the sorted dataset:
126, 127, 127, 128, 128
Median = (127 + 127) / 2 = 127
Q3 = 127
Now, we can find the interquartile range:
Interquartile Range = Q3 - Q1 = 127 - 125 = 2
Therefore, the range is 6, and the interquartile range is 2.