Question

using the following stem & leaf plot representing the time in minutes that a person commutes to work, find the five number summary, range and interquartile range for the data.
min=
q₁=
med=
q₃=
max=
range=
interquartile range=

Explanation:

Step1: Write out the data set

From the stem - and - leaf plot, the data set is \(10,12,21,22,28,29,29,42,42,43,49,50,52,53,55,58,59,60,64\).

Step2: Find the minimum (\(Min\))

The minimum value is the first value in the ordered data set. \(Min = 10\).

Step3: Find the first quartile (\(Q_1\))

The formula for the position of \(Q_1\) is \(i=\frac{n + 1}{4}\), where \(n = 19\). \(i=\frac{19+1}{4}=5\). The \(5^{th}\) value in the ordered data set is \(Q_1 = 28\).

Step4: Find the median (\(Med\))

The formula for the position of the median is \(i=\frac{n + 1}{2}\). \(i=\frac{19+1}{2}=10\). The \(10^{th}\) value in the ordered data set is \(Med=43\).

Step5: Find the third quartile (\(Q_3\))

The formula for the position of \(Q_3\) is \(i=\frac{3(n + 1)}{4}\). \(i=\frac{3(19 + 1)}{4}=15\). The \(15^{th}\) value in the ordered data set is \(Q_3 = 55\).

Step6: Find the maximum (\(Max\))

The maximum value is the last value in the ordered data set. \(Max = 64\).

Step7: Calculate the range

The range formula is \(Range=Max - Min\). \(Range=64 - 10=54\).

Step8: Calculate the inter - quartile range

The inter - quartile range formula is \(IQR = Q_3-Q_1\). \(IQR=55 - 28 = 27\).

Answer:

\(Min = 10\), \(Q_1=28\), \(Med = 43\), \(Q_3=55\), \(Max = 64\), \(Range = 54\), \(Interquartile\ Range=27\)