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.
2.7, 1.5, 2.8, 3.7, 1.5, 3.5, 0.7, 2.1, 2.5, 1.8, 3.2, 1.8, 3.5, 1.1, 4.4
send data to excel
part: 0 / 2
part 1 of 2
(a) draw the boxplot for the given data.

Explanation:

Step1: Order the data

First, we order the data set: \(0.7, 1.1, 1.5, 1.5, 1.8, 1.8, 2.1, 2.5, 2.7, 2.8, 3.2, 3.5, 3.5, 3.7, 4.4\) (Wait, wait, the original data has 14 numbers? Wait, let's check: 2.7, 1.5, 2.8, 3.7, 1.5, 3.5, 0.7, 2.1, 2.5, 1.8, 3.2, 1.8, 3.5, 1.1, 4.4 – that's 15 numbers? Wait, 2.7,1.5,2.8,3.7,1.5,3.5,0.7,2.1,2.5,1.8,3.2,1.8,3.5,1.1,4.4 – 14? Wait, 0.7,1.1,1.5,1.5,1.8,1.8,2.1,2.5,2.7,2.8,3.2,3.5,3.5,3.7,4.4 – 15? Wait, let's count: 0.7 (1), 1.1 (2), 1.5 (3), 1.5 (4), 1.8 (5), 1.8 (6), 2.1 (7), 2.5 (8), 2.7 (9), 2.8 (10), 3.2 (11), 3.5 (12), 3.5 (13), 3.7 (14), 4.4 (15). Yes, 15 data points.

Step2: Find Quartiles

• Minimum: \(0.7\)
• Q1 (25th percentile): The median of the first half. The first half (excluding median if odd) is the first 7 numbers: \(0.7, 1.1, 1.5, 1.5, 1.8, 1.8, 2.1\). The median of these 7 is the 4th term: \(1.5\)
• Median (50th percentile): The 8th term (since 15 terms, (15+1)/2 = 8th term) of the ordered data: \(2.5\)
• Q3 (75th percentile): The median of the second half. The second half (excluding median) is the last 7 numbers: \(2.7, 2.8, 3.2, 3.5, 3.5, 3.7, 4.4\). The median of these 7 is the 4th term: \(3.5\)
• Maximum: \(4.4\)

Step3: Draw Boxplot

• The box goes from Q1 (\(1.5\)) to Q3 (\(3.5\)), with a line at the median (\(2.5\)).
• The whiskers go from minimum (\(0.7\)) to Q1, and Q3 to maximum (\(4.4\)).
• Check for outliers: Using IQR = Q3 - Q1 = \(3.5 - 1.5 = 2.0\). Lower fence: Q1 - 1.5IQR = \(1.5 - 3 = -1.5\) (no lower outliers). Upper fence: Q3 + 1.5IQR = \(3.5 + 3 = 6.5\). The data point \(4.4\) is below 6.5, so no upper outliers.

Now, on the given axis (0 - 10, with ticks at 0,1,2,3,4,5,6,7,8,9,10), we plot:

• Minimum: 0.7 (near 0 - 1)
• Q1: 1.5 (between 1 and 2)
• Median: 2.5 (between 2 and 3)
• Q3: 3.5 (between 3 and 4)
• Maximum: 4.4 (between 4 and 5? Wait, no, 4.4 is between 4 and 5? Wait, 0.7, 1.5, 2.5, 3.5, 4.4. Wait, maybe the initial plot has some markers, but based on calculations, the box should be from ~1.5 to ~3.5, median at 2.5, whiskers from 0.7 to 4.4.

Answer:

To draw the boxplot, we use the five - number summary: Minimum = \(0.7\), \(Q_1 = 1.5\), Median = \(2.5\), \(Q_3 = 3.5\), Maximum = \(4.4\). The box spans from \(Q_1 = 1.5\) to \(Q_3 = 3.5\) with a line at the median (\(2.5\)). The left whisker extends from \(0.7\) to \(Q_1 = 1.5\) and the right whisker extends from \(Q_3 = 3.5\) to \(4.4\). (Note: Since the problem involves drawing, the key is to plot these values on the given axis with the box between \(1.5\) and \(3.5\), median at \(2.5\), and whiskers to \(0.7\) and \(4.4\))