A meteorologist recorded the following temperatures: {71,74,81,78,67,69,64}. Today's temperature is 67º. If today's temperature is included in the dataset, how does it change the interquartile range?

Answer 1

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.

First, we need to find the Q1 and Q3 values of the dataset {71,74,81,78,67,69,64}.

To find Q1:
1. Arrange the data in ascending order: {64,67,69,71,74,78,81}
2. Find the median of the lower half of the data: Q1 = (69+71) / 2 = 70

To find Q3:
1. Find the median of the upper half of the data: Q3 = (74+78) / 2 = 76

Now, calculate the IQR before including today's temperature:
IQR = Q3 - Q1 = 76 - 70 = 6

If today's temperature of 67º is included in the dataset, the new dataset will be {71,74,81,78,67,69,64,67}.

To find the new Q1 and Q3 values:
To find Q1:
1. Arrange the new data in ascending order: {64,67,67,69,71,74,78,81}
2. Find the median of the lower half of the new data: Q1 = (67+69) / 2 = 68

To find Q3:
1. Find the median of the upper half of the new data: Q3 = (74+78) / 2 = 76

Now, calculate the new IQR after including today's temperature:
IQR = Q3 - Q1 = 76 - 68 = 8

Therefore, including today's temperature of 67º in the dataset increases the interquartile range from 6 to 8.