Question

following boxplot displays the number of cars spotted on a road at the same time in a month.

1. what percent of the data is between 12 and 17 cars?
2. what is the minimum number, below which any value will be an outlier?

Explanation:

Step1: Recall box - plot properties

In a box - plot, the box represents the inter - quartile range (IQR). The left - hand side of the box is \(Q_1\), the middle line is \(Q_2\) (median), and the right - hand side is \(Q_3\). The whiskers extend to non - outlier data points. The formula for IQR is \(IQR=Q_3 - Q_1\). Also, the lower fence for outliers is \(Q_1-1.5\times IQR\) and the upper fence is \(Q_3 + 1.5\times IQR\).

Step2: Analyze the box - plot for the first question

From the box - plot, assume \(Q_1 = 12\) and \(Q_3=16\). The median \(Q_2\) divides the data into two halves. The part of the box from \(Q_1\) to \(Q_3\) (the IQR) represents \(50\%\) of the data. The part from \(Q_3\) to the end of the right - hand whisker (up to non - outlier values) represents \(25\%\) of the data. Since \(17\) is on the right - hand whisker (assuming non - outlier), the data between \(12\) and \(17\) is \(50\%+25\%=75\%\)

Step3: Analyze the box - plot for the second question

First, find \(IQR\). Let \(Q_1 = 12\) and \(Q_3 = 16\), so \(IQR=Q_3 - Q_1=16 - 12 = 4\). The lower fence for outliers is \(Q_1-1.5\times IQR\). Substitute the values: \(12-1.5\times4=12 - 6=6\)

Answer:

1. \(75\%\)
2. \(6\)