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. 2.5, 2.5, 3, 4, 0.7, 2.2, 4.6, 0.7, 0.8, 3.7, 3.4, 3.9 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: \(0.7, 0.7, 0.8, 2.2, 2.5, 2.5, 3, 3.4, 3.7, 3.9, 4, 4.6\)

Step2: Find the median (Q2)

The number of data points \(n = 12\) (even), so the median is the average of the 6th and 7th values.
6th value: \(2.5\), 7th value: \(3\)
Median \(Q2=\frac{2.5 + 3}{2}=2.75\)

Step3: Find Q1 (median of lower half)

Lower half data: \(0.7, 0.7, 0.8, 2.2, 2.5, 2.5\) (6 values, even)
Median of lower half: average of 3rd and 4th values.
3rd value: \(0.8\), 4th value: \(2.2\)
\(Q1=\frac{0.8 + 2.2}{2}=1.5\)

Step4: Find Q3 (median of upper half)

Upper half data: \(3, 3.4, 3.7, 3.9, 4, 4.6\) (6 values, even)
Median of upper half: average of 3rd and 4th values.
3rd value: \(3.7\), 4th value: \(3.9\)
\(Q3=\frac{3.7 + 3.9}{2}=3.8\)

Step5: Find Min and Max

Minimum value (Min): \(0.7\)
Maximum value (Max): \(4.6\)

Step6: Draw the boxplot

• The box spans from \(Q1 = 1.5\) to \(Q3 = 3.8\), with a line at the median \(Q2 = 2.75\).
• The whiskers extend from Min (\(0.7\)) to \(Q1\) and from \(Q3\) to Max (\(4.6\)).

Answer:

To draw the boxplot:

• The left whisker starts at \(0.7\) (min) and ends at \(Q1 = 1.5\).
• The box starts at \(Q1 = 1.5\), has a line at median \(2.75\), and ends at \(Q3 = 3.8\).
• The right whisker starts at \(Q3 = 3.8\) and ends at \(4.6\) (max).

(Note: The given initial boxplot in the image seems to have incorrect markings; the correct boxplot should be drawn using the calculated \(Q1 = 1.5\), \(Q2 = 2.75\), \(Q3 = 3.8\), Min \(= 0.7\), Max \(= 4.6\))