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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Box and Whisker Plots, Identifying Outliers

Grade: 1300-a Lesson: S4-L6

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Make a box-and-whisker plot that represents the data. Describe the distribution. Video game prices (in dollars): 45, 40, 50, 35, 30, 40, 40, 30, 45, and 6.
2	Step	First, order the data in ascending order: 6, 30, 30, 35, 40, 40, 40, 45, 45, and 50.
3	Step	Calculate the Five-Number Summary. → Minimum: 6. → First Quartile (Q1): The median of the lower half (excluding the overall median) Q1 = Median of {6, 30, 30, 35, and 40} = 30. → Median (Q2): The median of the entire data set Q2 = Median of {6, 30, 30, 35, 40, 40, 40, 45, 45, and 50} = \$40 + 40 / 2\$ = 40. → Third Quartile (Q3): The median of the upper half (excluding the overall median) Q3 = Median of {40, 45, 45, and 50} = 45. → Maximum: 50.
4	Step	Description of the Distribution. To determine if the distribution is symmetric, skewed left, or skewed right, we analyze the positioning of the median and the quartiles: → Left-skewed distribution: If the left whisker is longer than the right whisker and the median is closer to Q3. → Right-skewed distribution: If the right whisker is longer than the left whisker and the median is closer to Q1. → Symmetric distribution: If the whiskers are roughly equal in length and the median is centered in the box.
5	Step	Given our data. → The left whisker (6 to 30) is much longer than the right whisker (45 to 50). → The median (40) is closer to Q3 (45) than to Q1 (30).
6	Step	So, the distribution is Skewed Left.
7	Choice.A	A symmetric distribution has equal-length whiskers on both sides of the box and the median is centered within the box. The box itself is also symmetric around the median	Symmetric
8	Choice.B	A left-skewed distribution has a longer left whisker than the right whisker, and the median is closer to Q3 (right side of the box). This indicates that a few low outlier values are pulling the distribution to the left	Skewed Left
9	Choice.C	A right-skewed distribution has a longer right whisker than the left whisker, and the median is closer to Q1 (left side of the box). This indicates that a few high outlier values are pulling the distribution to the right	Skewed Right
10	Choice.D	This option would be chosen if the data does not fit into any of the above categories. For instance, if the distribution is highly irregular or if there’s an unusual pattern that doesn’t conform to standard skewness or symmetry	None of the above
11	Answer	Option	B
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

Make a box-and-whisker plot that represents the data. Describe the distribution. Video game prices (in dollars): 45, 40, 50, 35, 30, 40, 40, 30, 45, and 6.

Step

First, order the data in ascending order: 6, 30, 30, 35, 40, 40, 40, 45, 45, and 50.

Step

Calculate the Five-Number Summary.

→ Minimum: 6.

→ First Quartile (Q1): The median of the lower half (excluding the overall median)
Q1 = Median of {6, 30, 30, 35, and 40} = 30.

→ Median (Q2): The median of the entire data set
Q2 = Median of {6, 30, 30, 35, 40, 40, 40, 45, 45, and 50} = \$40 + 40 / 2\$ = 40.

→ Third Quartile (Q3): The median of the upper half (excluding the overall median)
Q3 = Median of {40, 45, 45, and 50} = 45.

→ Maximum: 50.

Step

Description of the Distribution.
To determine if the distribution is symmetric, skewed left, or skewed right, we analyze the positioning of the median and the quartiles:

→ Left-skewed distribution: If the left whisker is longer than the right whisker and the median is closer to Q3.

→ Right-skewed distribution: If the right whisker is longer than the left whisker and the median is closer to Q1.

→ Symmetric distribution: If the whiskers are roughly equal in length and the median is centered in the box.

Step

Given our data.

→ The left whisker (6 to 30) is much longer than the right whisker (45 to 50).
→ The median (40) is closer to Q3 (45) than to Q1 (30).

Step

So, the distribution is Skewed Left.

Choice.A

A symmetric distribution has equal-length whiskers on both sides of the box and the median is centered within the box. The box itself is also symmetric around the median

Symmetric

Choice.B

A left-skewed distribution has a longer left whisker than the right whisker, and the median is closer to Q3 (right side of the box). This indicates that a few low outlier values are pulling the distribution to the left

Skewed Left

Choice.C

A right-skewed distribution has a longer right whisker than the left whisker, and the median is closer to Q1 (left side of the box). This indicates that a few high outlier values are pulling the distribution to the right

Skewed Right

Choice.D

This option would be chosen if the data does not fit into any of the above categories. For instance, if the distribution is highly irregular or if there’s an unusual pattern that doesn’t conform to standard skewness or symmetry

None of the above

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?