MATH SOLVE

4 months ago

Q:
# 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

Accepted Solution

A:

Answer:Minimum value = 43, [tex]Q_1=52[/tex], [tex]Q_2=Median=61[/tex], [tex]Q_3=67[/tex], Maximum value = 69.Distribution is negative skewed.Step-by-step explanation:The given data set is44, 43, 67, 68, 57, 65, 52, 62, 69, 54, 53, 61, 67, 48, 65Arrange the data in ascending order43, 44, 48, 52, 53, 54, 57, 61, 62, 65, 65, 67, 67, 68, 69Divide the data in 4 equal parts.(43, 44, 48), 52, (53, 54, 57), 61, (62, 65, 65), 67, (67, 68, 69)Minimum value = 43[tex]Q_1=52[/tex][tex]Q_2=Median=61[/tex][tex]Q_3=67[/tex]Maximum value = 69Starting 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 [tex]Q_3-Q_2=Q_2-Q_1[/tex]Positive skew: If [tex]Q_3-Q_2>Q_2-Q_1[/tex]Negative skew: If [tex]Q_3-Q_2<Q_2-Q_1[/tex]For the given data set [tex]Q_3-Q_2=67-61=6[/tex][tex]Q_2-Q_1=61-52=9[/tex]Since [tex]Q_3-Q_2<Q_2-Q_1[/tex], therefore the given distribution is negative skewed.