In: Statistics and Probability
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
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.