Question

based on the following calculator output, determine the inter - quartile range of the dataset.
1 - var - stats
$overline{x}=98.22641509433963$
$sum x = 15618$
$sum x^{2}=1603212$
$sx = 20.914510899876102$
$sigma x = 20.84863826097835$
$n = 159$
$minx = 36$
$q_{1}=85$
$med = 98$
$q_{3}=111$
$maxx = 147$

Explanation:

Step1: Recall the formula for inter - quartile range

The inter - quartile range (IQR) is given by the formula \(IQR = Q_{3}-Q_{1}\), where \(Q_{1}\) is the first quartile and \(Q_{3}\) is the third quartile.

Step2: Identify the values of \(Q_{1}\) and \(Q_{3}\)

From the calculator output, \(Q_{1}=85\) and \(Q_{3}=111\).

Step3: Calculate the inter - quartile range

Substitute the values of \(Q_{1}\) and \(Q_{3}\) into the formula: \(IQR=111 - 85\).

Answer:

\(26\)