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Lesson Example Discussion Quiz: Class Homework

Step-1

Title: Box and Whisker Plots, Identifying Outliers

Grade: 1400-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	The data set shows the prices (in dollars) of lacrosse helmets. Make a box-and-whisker plot that represents the data. Describe the distribution. 125, 120, 250, 110, 190, 220, 145, 260, 240, 150, 170, and 200.
2	Step	The given data is ordered in ascending order: 110, 120, 125, 145, 150, 170, 190, 200, 220, 240, 250, and 260.
3	Step	Calculate the Five-Number Summary → Minimum: The smallest value in the data set is 110. → First Quartile (Q1): The median of the lower half of the data Q1 = Median of {110, 120, 125, 145, 150, and 170} \$= 125 + 145 / 2\$ = 135 → Median (Q2): The median of the entire data set Q2 = Median of {110, 120, 125, 145, 150, 170, 190, 200, 220, 240, 250, and 260} \$= 170 + 190 / 2\$ = 180 → Third Quartile (Q3): The median of the upper half of the data Q3 = Median of {190, 200, 220, 240, 250, and 260} \$= 220 + 240 / 2\$ = 230 → Maximum: The largest value in the data set is 260.
4	Step	Constructing the Box-and-Whisker Plot. → Draw a number line that covers the range of your data, from 110 to 260. → Draw a box from Q1 (135) to Q3 (230). → Draw a line inside the box at the median (180). → Extend "whiskers" from the edges of the box to the minimum value (110) and the maximum value (260).
5	Step	Description of the Distribution. → The data is spread out with prices ranging from $110 to $260. → The middle 50% of the data (between Q1 and Q3) ranges from $135 to $230, showing a broad interquartile range (IQR) of 95. → The whiskers are almost symmetric around the median, suggesting a roughly symmetric distribution with no extreme outliers.
6	Choice.A	This plot correctly depicts a box-and-whisker plot for the lacrosse helmet price data. The minimum value (least price) is represented by the leftmost point on the number line. The box shows the spread of the data between Q1 and Q3. The line in the middle of the box represents the median (Q2). The whiskers extend from the box towards the minimum and maximum values, likely following the 1.5 IQR rule from the quartiles	$1.1$
7	Choice.B	The box in this plot is wider than expected for the IQR, and the whiskers extend to data points that might be outliers but are included within the whiskers	$1.2$
8	Choice.C	The median line is missing in the box, and the whiskers seem to extend beyond potential outliers	$1.3$
9	Choice.D	The box is too short, and the left whisker extends to a data point that likely falls within the 1.5 IQR range	$1.4$
10	Answer	Option	A
11	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

The data set shows the prices (in dollars) of lacrosse helmets. Make a box-and-whisker plot that represents the data. Describe the distribution.
125, 120, 250, 110, 190, 220, 145, 260, 240, 150, 170, and 200.

Step

The given data is ordered in ascending order:
110, 120, 125, 145, 150, 170, 190, 200, 220, 240, 250, and 260.

Step

Calculate the Five-Number Summary

→ Minimum: The smallest value in the data set is 110.

→ First Quartile (Q1): The median of the lower half of the data
Q1 = Median of {110, 120, 125, 145, 150, and 170}
\$= 125 + 145 / 2\$ = 135

→ Median (Q2): The median of the entire data set
Q2 = Median of {110, 120, 125, 145, 150, 170, 190, 200, 220, 240, 250, and 260}
\$= 170 + 190 / 2\$ = 180

→ Third Quartile (Q3): The median of the upper half of the data
Q3 = Median of {190, 200, 220, 240, 250, and 260}
\$= 220 + 240 / 2\$ = 230

→ Maximum: The largest value in the data set is 260.

Step

Constructing the Box-and-Whisker Plot.

→ Draw a number line that covers the range of your data, from 110 to 260.
→ Draw a box from Q1 (135) to Q3 (230).
→ Draw a line inside the box at the median (180).
→ Extend "whiskers" from the edges of the box to the minimum value (110) and the maximum value (260).

Step

Description of the Distribution.

→ The data is spread out with prices ranging from $110 to $260.
→ The middle 50% of the data (between Q1 and Q3) ranges from $135 to $230, showing a broad interquartile range (IQR) of 95.
→ The whiskers are almost symmetric around the median, suggesting a roughly symmetric distribution with no extreme outliers.

Choice.A

This plot correctly depicts a box-and-whisker plot for the lacrosse helmet price data. The minimum value (least price) is represented by the leftmost point on the number line. The box shows the spread of the data between Q1 and Q3. The line in the middle of the box represents the median (Q2). The whiskers extend from the box towards the minimum and maximum values, likely following the 1.5 IQR rule from the quartiles

$1.1$

Choice.B

The box in this plot is wider than expected for the IQR, and the whiskers extend to data points that might be outliers but are included within the whiskers

$1.2$

Choice.C

The median line is missing in the box, and the whiskers seem to extend beyond potential outliers

$1.3$

Choice.D

The box is too short, and the left whisker extends to a data point that likely falls within the 1.5 IQR range

$1.4$

Answer

Option

Sumup

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