Question

The data represent the age of world leaders on their day of inauguration. Find the five-number summary, and construct a boxplot for the data. Comment on the shape of the distribution.

60 56 47 59

64 68 57 45

65 64 62 48

63 68 69

The five-number summary is _____

(Use ascending order)

Draw the boxplot

What is the shape of the distribution?

- Rougly symmetric

-Skewed to the left

-Skewed to the right

-Shape of the distribution cannot be determined from the boxplot

Answer 1

The five-number summary for age of world leaders on their day of inauguration is obtained in excel. The screenshot is shown below,

The number summary is,

Minimum	45
first quartile	56
median	62
Third quartil	65
Maximum	69

The box plot is obtained in excel by following these steps,

Step 1: Make a column "Difference" and take difference of each consecutive row,

Step 2: Now, select difference column then INSERT > Recommended Charts > Bar > Staked Bar. The screenshot is shown below,

The screenshot for chart is shown below,

Step 3: Click on the outer boxes > Right click > No Fill. The screenshot is shown below,

Step 4: Click on the right box > Add Chart Element > Error Bar > More Options > OK. The screenshot is shown below,

Step 5: Select Horizontal Error Bar > Error Amount > Custom > Positive Error Value = 4 (because difference between maximum value and third quartile is 4), negative Error Value = 0. The screenshot is shown below,

Step 6: Similarly, Click on the left box > Add Chart Element > Error Bar > More Options > OK then Select Horizontal Error Bar > Error Amount > Custom > Positive Error Value = 0, negative Error Value = 11 The screenshot is shown below,

The box plot is obtained. The screenshot is shown below,

Shape of the distribution

Answer: Skewed to the left

Explanation: From the box plot we can see that, the size of left box is wider than than left box hence the distribution of data values are skewed to left.