Skews and observation of box plot

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section: Chapter Questions
Problem 6CR
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Skews and observation of box plot
Variable: the amount of doctors per 10k people.
Mean: 21.6
Standard deviation: 17.59
Range of "Usual Values": 13.58 – 56.78
5- number summary:
Min: 0.1
Q1: 5.6
Median: 20.6
Q3: 32
Маx: 84.2
Воx plot:
Doctors per 10k
5.6
20.6
32
84.2
15
30
45
60
75
Transcribed Image Text:Variable: the amount of doctors per 10k people. Mean: 21.6 Standard deviation: 17.59 Range of "Usual Values": 13.58 – 56.78 5- number summary: Min: 0.1 Q1: 5.6 Median: 20.6 Q3: 32 Маx: 84.2 Воx plot: Doctors per 10k 5.6 20.6 32 84.2 15 30 45 60 75
Expert Solution
Step 1

Boxplot:

Boxplot is the simple way to plot the observations of the distribution, with five-number summary of order, minimum, first quartile Q1, median Q2, third quartile Q3, maximum. The boxplot can be used for determining whether the shape of the distribution is symmetric or skewed.

In the boxplot, border line towards the left side (bottom) of the box represents the value of first quartile. The median is the middle value of the data set. In the boxplot, the line in middle of the box represents median of the dataset. The border line towards the right side (top) of the box represents the value of third quartile. The point from where the lower whisker (left) starts is the minimum value and the point where the upper whisker (right) ends is the maximum value 

Shape of distribution using boxplot:

The distribution of data would be positively skewed (skewed right) when the center line (median) is closer to the left side (lower end) of the box.
The distribution of data would be negatively skewed (skewed left) when the center line (median) is closer to the right side (upper end) of the box.
The distribution of data would be symmetric when the center line (median) is at the center of box. The median divides the boxplot into to equal parts.

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