Question

i can compare two groups of numeric data.
in pleasantville, texas there are two annual
parades, the 4th of july parade and new years
day parade. the box plots show the number
of floats in each parade over the past 15
years.

1. fill in the blanks below to make each

statement true.
a. the range of the data in the 4th of july
parade is ______________ the range of
the data in the new years day parade.
b. the median number of floats in the new
years day parade is ______________
the median number of floats in the 4th of july
parade.
c. the interquartile range for the 4th of july
parade is ______________ than the new years
day parade.

1. how would you describe the shape of the 4th of july parade? the new years day parade?

Explanation:

Step1: Find the range

The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \).
For the \(4^{th}\) of July parade:

• Minimum \( = 8 \)
• Maximum \( = 28 \)
• Range \( = 28 - 8=20 \)

For the New Year's Day parade:

• Minimum \( = 6 \)
• Maximum \( = 24 \)
• Range \( = 24 - 6 = 18 \)

Since \(20>18\), the range of the \(4^{th}\) of July parade is greater than the range of the New Year's Day parade.

Step2: Find the median

The median is the middle - value of the data set (the line inside the box of the box - plot).
For the \(4^{th}\) of July parade:

• Median \( = 17 \)

For the New Year's Day parade:

• Median \( = 13 \)

Since \(13<17\), the median number of floats in the New Year's Day parade is less than the median number of floats in the \(4^{th}\) of July parade.

Step3: Find the inter - quartile range

The inter - quartile range (IQR) is calculated as \( \text{IQR}=Q_{3}-Q_{1} \) (where \(Q_{3}\) is the upper quartile and \(Q_{1}\) is the lower quartile).
For the \(4^{th}\) of July parade:

• \(Q_{1}=12\), \(Q_{3}=22\)
• \(IQR = 22 - 12=10\)

For the New Year's Day parade:

• \(Q_{1}=9\), \(Q_{3}=19\)
• \(IQR = 19 - 9 = 10\)

Since \(10 = 10\), the inter - quartile range for the \(4^{th}\) of July parade is equal to the New Year's Day parade.

Step4: Describe the shape

For the \(4^{th}\) of July parade:

• The left whisker is longer than the right whisker. So, it is skewed left (negatively skewed).

For the New Year's Day parade:

• The right whisker is longer than the left whisker. So, it is skewed right (positively skewed).

Answer:

a. greater than
b. less than
c. equal
11.

• The \(4^{th}\) of July parade is skewed left (negatively skewed).
• The New Year's Day parade is skewed right (positively skewed).