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, 40, 45, 45, and 50} = 45
→ Maximum: 50

4

Step

Construct the Box-and-Whisker Plot:

Based on the five-number summary, we can construct the plot
→ Draw a number line that covers the range from the minimum value (6) to the maximum value (50).
→ Draw a box from Q1 (30) to Q3 (45).
→ Draw a line inside the box at the median (40).
→ Extend "whiskers" from the edges of the box to the minimum value (6) and the maximum value (50).

5

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.

6

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).

7

Solution

So, the distribution is Skewed Left.

8

Sumup

Please summarize steps

Choices

9

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

Wrong Symmetric

10

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 so this option is correct

Correct Skewed Left

11

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

Wrong Skewed Right

12

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

Wrong None of the above

13

Answer

Option

B

14

Sumup

Please summarize choices