Question

based on the following calculator output, determine the inter - quartile range of the dataset.
1 - var - stats
\\(\bar{x} = 272.3609022556391\\)
\\(\sigma x = 36224\\)
\\(\sigma x^{2} = 9916490\\)
\\(sx = 19.557350918192967\\)
\\(\sigma x = 19.483688317773158\\)
\\(n = 133\\)
\\(\text{min}x = 226\\)
\\(q_{1} = 260.5\\)
\\(\text{med} = 274\\)
\\(q_{3} = 283\\)
\\(\text{max}x = 328\\)

Explanation:

Step1: Recall IQR formula

The inter - quartile range (IQR) is calculated as \(IQR = Q_3 - Q_1\).

Step2: Identify \(Q_1\) and \(Q_3\) from the output

From the calculator output, we have \(Q_1 = 260.5\) and \(Q_3 = 283\).

Step3: Calculate IQR

Substitute the values of \(Q_1\) and \(Q_3\) into the formula: \(IQR=283 - 260.5 = 22.5\).

Answer:

\(22.5\)