Question

the following data represent the number (in millions) of visitors who traveled to a foreign country each year for a random selection of years. 4.8, 4.3, 2.6, 1.8, 4.9, 3.3, 1.6, 2, 3.2, 4.5 send data to excel part: 0 / 2 part 1 of 2 (a) draw the boxplot for the given data. visitors (in millions)

Explanation:

Step1: Order the data

First, we order the data set: \(1.6, 1.8, 2, 2.6, 3.2, 3.3, 4.3, 4.5, 4.8, 4.9\) (Wait, wait, original data: \(4.8, 4.3, 2.6, 1.8, 4.9, 3.3, 1.6, 2, 3.2, 4.5\) – let's re - order correctly: \(1.6, 1.8, 2, 2.6, 3.2, 3.3, 4.3, 4.5, 4.8, 4.9\) (Wait, the number of data points: let's count. The data is \(4.8, 4.3, 2.6, 1.8, 4.9, 3.3, 1.6, 2, 3.2, 4.5\) – that's 10 data points? Wait, no: \(4.8,4.3,2.6,1.8,4.9,3.3,1.6,2,3.2,4.5\) – 10 values? Wait, no, let's count again: 1.6, 1.8, 2, 2.6, 3.2, 3.3, 4.3, 4.5, 4.8, 4.9 – 10 values. Wait, but to find quartiles, for \(n = 10\) (even), \(Q_1\) is the median of the first 5, \(Q_3\) is the median of the last 5.

First, order the data: \(1.6, 1.8, 2, 2.6, 3.2, 3.3, 4.3, 4.5, 4.8, 4.9\)

Step2: Find the median (second quartile, \(Q_2\))

Since \(n = 10\) (even), the median is the average of the 5th and 6th values. The 5th value is \(3.2\), the 6th is \(3.3\), so \(Q_2=\frac{3.2 + 3.3}{2}=3.25\)

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

The first half of the data (first 5 values): \(1.6, 1.8, 2, 2.6, 3.2\). The median of these 5 (odd number) is the 3rd value, so \(Q_1 = 2\)

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

The second half of the data (last 5 values): \(3.3, 4.3, 4.5, 4.8, 4.9\). The median of these 5 is the 3rd value, so \(Q_3 = 4.5\)

Step5: Find the minimum and maximum

Minimum value: \(1.6\), Maximum value: \(4.9\)

Now, to draw the box - plot:

• The box spans from \(Q_1 = 2\) to \(Q_3 = 4.5\), with a line inside the box at \(Q_2=3.25\)
• The whiskers extend from the minimum (\(1.6\)) to \(Q_1\) and from \(Q_3\) to the maximum (\(4.9\))

Answer:

To draw the box - plot:

• Minimum: \(1.6\)
• \(Q_1\): \(2\)
• Median (\(Q_2\)): \(3.25\)
• \(Q_3\): \(4.5\)
• Maximum: \(4.9\)

The box is drawn between \(x = 2\) and \(x = 4.5\), with a vertical line at \(x = 3.25\). The left whisker goes from \(x = 1.6\) to \(x = 2\), and the right whisker goes from \(x = 4.5\) to \(x = 4.9\)