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

Minimum value = 43, , , , 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

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

Positive skew: If

Negative skew: If

For the given data set

Since , therefore the given distribution is negative skewed.

a - base

b - exponent

so,