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.44, 43, 67, 68, 57, 65, 52, 62, 69, 54, 53, 61, 67, 48, 65​

Answer 1

Answer:

Minimum value = 43, $Q_1=52$, $Q_2=Median=61$, $Q_3=67$, Maximum value = 69.

Distribution is negative skewed.

Step-by-step explanation:

The given data set is

44, 43, 67, 68, 57, 65, 52, 62, 69, 54, 53, 61, 67, 48, 65​

Arrange the data in ascending order

43, 44, 48, 52, 53, 54, 57, 61, 62, 65, 65, 67, 67, 68, 69

Divide the data in 4 equal parts.

(43, 44, 48), 52, (53, 54, 57), 61, (62, 65, 65), 67, (67, 68, 69)

Minimum value = 43

$Q_1=52$

$Q_2=Median=61$

$Q_3=67$

Maximum value = 69

Starting and end point of box plot represent the minimum and maximum value respectively. Box starts from the first quartile to the third quartile. A vertical line goes through the box at the median.

The shape of the distribution.

Normally distributed: If $Q_3-Q_2=Q_2-Q_1$

Positive skew: If $Q_3-Q_2>Q_2-Q_1$

Negative skew: If $Q_3-Q_2<Q_2-Q_1$

For the given data set

$Q_3-Q_2=67-61=6$

$Q_2-Q_1=61-52=9$

Since $Q_3-Q_2<Q_2-Q_1$, therefore the given distribution is negative skewed.