Question

What is the interquartile range of the data?

120, 140, 150, 195, 203, 226, 245, 280

Answer 1

The interquartile range (IQR) of the data set (120, 140, 150, 195, 203, 226, 245, 280) is calculated as the difference between the third quartile and the first quartile, which results in an IQR of 90.5.

Step-by-step explanation:

Calculating the Interquartile Range (IQR)

The interquartile range (IQR) represents the spread of the middle 50 percent of a data set, calculated as the difference between the third quartile (Q3) and the first quartile (Q1), that is, IQR = Q3 - Q1. To find the IQR for the provided data set (120, 140, 150, 195, 203, 226, 245, 280), first we must locate Q1 and Q3. Since there are eight data points, Q1 is the average of the 2nd and 3rd values (140 and 150) and Q3 is the average of the 6th and 7th values (226 and 245). So Q1 = (140 + 150) / 2 = 145 and Q3 = (226 + 245) / 2 = 235.5.

The IQR is then 235.5 - 145 = 90.5.

The IQR is used to identify the central tendency and potential outliers within a set of data, with outliers being defined as values more than 1.5 × IQR above Q3 or below Q1.

Answer 2

Let me rewrite it :(120, 140, 150,) 195, 203,( 226, 245, 280)

1) Find the Median: Since the number of data points are even, the Median will be the average of the terms 195 & 203, that is

Median = (195+203)/2 =199
Now find the Median value of the lower & upper part (between parenthesis)
Median Lower Part = 140 ==> it's called Q₁
Median Upper part = 245 ==> it's called Q₃
The interquartile range = IQR = Q₃-Q₁ =245 - 140 ==> 105
Remark: The Q₂ is nothing but the central value (in our case it's the median calculated at 199)