Question

the stemplot below displays the arm spans, in centimeters, for 20 students. identify the outliers, if they exist.
there are no outliers.
153
202
192, 202
arm span (cm)
key: 11|6 = 16 cm

Explanation:

Step1: List the data

The data values from the stemplot are: \(153,155,156,160,162,162,162,163,163,165,166,167,170,173,180,181,182,189,192,202\)

Step2: Find quartiles

First, find the median (\(Q_2\)). Since \(n = 20\), \(Q_2=\frac{10^{th}+11^{th}}{2}=\frac{165 + 166}{2}=165.5\)
Lower half: \(153,155,156,160,162,162,162,163,163,165\). \(Q_1=\frac{5^{th}+6^{th}}{2}=\frac{162+162}{2} = 162\)
Upper half: \(166,167,170,173,180,181,182,189,192,202\). \(Q_3=\frac{5^{th}+6^{th}}{2}=\frac{180 + 181}{2}=180.5\)

Step3: Calculate IQR

\(IQR=Q_3 - Q_1=180.5-162 = 18.5\)

Step4: Find fences

Lower fence: \(Q_1-1.5IQR=162-1.5\times18.5=162 - 27.75=134.25\)
Upper fence: \(Q_3 + 1.5IQR=180.5+1.5\times18.5=180.5+27.75 = 208.25\)

Answer:

There are no outliers.