Question

Find the range and IQR of the data.

Answer 1

Calculation:
Range:
It is the difference between the maximum and the minimum values is termed as range.
Range \(= max - min\)
Here the maximum value is 180 and the minimum value is 120.
Range \(= max - min\)
\(= 180-120= \$60\)
Thus, the range is \(\$60\).
Inter quartile range:
In contrast to the range, which measures only differences between the extremes, the inter quartile range (also called mid spread) is the difference between the third quartile and the first quartile. Thus, it measures the variation in the middle 50 percent ofjthe data and unlike the range it is not affected by extreme values. \(IQR=Q_{3}-Q_{1}\).
Substitute \(Q_{1},\ as\ 125\ and\ Q_{3}\) as 155 in the above formula,
\(IQR = 155 — 125= \$30\)
Thus, the IQR for the cost of compact refrigerators is \(\$30\).