Question

sara is practicing speed pole climbing. the data show her times in seconds.
16 17.5 17 18 16.5 17 20
saras range = 4 seconds
the range is one way to measure variability.
it describes how spread out all the data is.
the interquartile range (iqr) is another way to measure variability.
the iqr describes how spread out the middle 50% of the data is.
iqr = q3 - q1
what is the interquartile range (iqr) for saras data set?
saras iqr = seconds

Explanation:

Step1: Sort the data

Sort the data set \(16, 17.5, 17, 18, 16.5, 17, 20\) in ascending order: \(16, 16.5, 17, 17, 17.5, 18, 20\).

Step2: Find \(Q1\) and \(Q3\)

The median of the lower half (first \(3\) values) is \(Q1\). For \(16, 16.5, 17\), \(Q1 = 16.5\).
The median of the upper half (last \(3\) values) is \(Q3\). For \(17.5, 18, 20\), \(Q3 = 18\).

Step3: Calculate the IQR

Use the formula \(IQR=Q3 - Q1\). Substitute \(Q1 = 16.5\) and \(Q3 = 18\) into the formula: \(IQR=18 - 16.5\).

Answer:

\(1.5\)