Question

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.

Answer 1

To find the range of the dataset, we need to find the difference between the highest and lowest values.

The highest value in the dataset is 129 and the lowest value is 123.

Range = 129 - 123 = 6

To find the interquartile range (IQR) of the dataset, we first need to find the first quartile (Q1) and the third quartile (Q3).

Q1 is the median of the lower half of the dataset. Since there are 10 values, Q1 is the median of the first 5 values in ascending order.
125, 125, 123, 126, 127
Q1 = (125 + 126) / 2 = 125.5

Q3 is the median of the upper half of the dataset.
127, 128, 128, 129
Q3 = (128 + 128) / 2 = 128

IQR = Q3 - Q1 = 128 - 125.5 = 2.5

Therefore, the range of the dataset is 6 and the interquartile range is 2.5.