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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​

User CyanAngel
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1 Answer

3 votes

Answer:

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

Distribution is negative skewed.

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.

The data represent the age of world leaders on their day of inauguration. Find the-example-1
User Thoean
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5.9k points