Question

create a box plot using the following set of data. 44,25,50,65,80,95,40,25,72,84,70

Explanation:

Step1: Order the data

First, we order the data set: \(25, 25, 40, 44, 50, 65, 70, 72, 80, 84, 95\)

Step2: Find the minimum and maximum

The minimum value is \(25\) (the smallest number in the ordered set) and the maximum value is \(95\) (the largest number).

Step3: Find the median (Q2)

Since there are \(11\) data points (odd number), the median is the middle value, which is the \(6^{th}\) value. So the median \(Q2 = 65\).

Step4: Find Q1 (median of the lower half)

The lower half of the data is \(25, 25, 40, 44, 50\) (the first \(5\) values). The median of this lower half is the \(3^{rd}\) value, so \(Q1 = 40\).

Step5: Find Q3 (median of the upper half)

The upper half of the data is \(70, 72, 80, 84, 95\) (the last \(5\) values). The median of this upper half is the \(3^{rd}\) value, so \(Q3 = 80\).

Step6: Draw the box plot

• The left whisker goes from the minimum (\(25\)) to \(Q1\) (\(40\)).
• The box goes from \(Q1\) (\(40\)) to \(Q3\) (\(80\)), with a line inside the box at the median (\(65\)).
• The right whisker goes from \(Q3\) (\(80\)) to the maximum (\(95\)).

Now, we place the points:

• The left dot (minimum) at \(25\).
• The left end of the box at \(40\), the right end of the box at \(80\), and the median line at \(65\).
• The right dot (maximum) at \(95\).

Answer:

The box plot should have:

• Minimum (left dot): at \(25\)
• \(Q1\) (left end of box): at \(40\)
• Median (line in box): at \(65\)
• \(Q3\) (right end of box): at \(80\)
• Maximum (right dot): at \(95\)

(Visually, the left dot is at the \(25\) mark, the box starts at \(40\), has a line at \(65\), ends at \(80\), and the right dot is at \(95\) on the number line provided.)