Question

which box plot represents the data set given? 20, 26, 34, 38, 42, 42, 46, 48. choose the correct answer. a) description of box - plot a with numbers on axis from 18 to 50 b) description of box - plot b with numbers on axis from 18 to 50 c) description of box - plot c with numbers on axis from 18 to 50 d) description of box - plot d with numbers on axis from 18 to 50

Explanation:

Step1: Find the minimum value

The minimum value in the data - set \(20,26,34,38,42,42,46,48\) is \(20\).

Step2: Find the first quartile (\(Q_1\))

First, order the data. There are \(n = 8\) data points. The position of \(Q_1\) is \(\frac{n + 1}{4}=\frac{8+1}{4}=2.25\). So, \(Q_1=26+(0.25)\times(34 - 26)=26 + 2=28\).

Step3: Find the median (\(Q_2\))

The position of the median for \(n = 8\) data points is \(\frac{n}{2}=4\) and \(\frac{n}{2}+1 = 5\). So, \(Q_2=\frac{38 + 42}{2}=40\).

Step4: Find the third quartile (\(Q_3\))

The position of \(Q_3\) is \(\frac{3(n + 1)}{4}=\frac{3\times(8 + 1)}{4}=6.75\). So, \(Q_3=42+(0.75)\times(46 - 42)=42+3 = 45\).

Step5: Find the maximum value

The maximum value in the data - set is \(48\).

Answer:

We need to check which box - plot has a minimum at \(20\), \(Q_1\) at \(28\), median at \(40\), \(Q_3\) at \(45\) and maximum at \(48\). Without seeing the visual differences in the provided box - plots in detail (assuming the correct scale and positions), we have calculated the key statistics for the data - set. If we assume the box - plots are drawn correctly with respect to the scale, we can match these values. But since no visual differences are described in the options, we note that the box - plot should have a left - most point at \(20\), the left - hand side of the box at \(28\), the line inside the box at \(40\), the right - hand side of the box at \(45\) and the right - most point at \(48\).