Answer :
Certainly! Let's walk through the solution step-by-step, focusing on understanding the relative frequencies associated with different price ranges. We will also address what these values might represent and how they can be interpreted.
### Step-by-Step Solution
1. Understanding Relative Frequency:
- Relative frequency is a measure that tells us the proportion of data points that fall within a particular interval or category out of the total number of data points. It's often expressed as a decimal or percentage.
2. Given Table:
- We have a table listing price ranges (in \[tex]$1000s) alongside their respective relative frequencies.
3. Interpreting the Table:
- Each price range indicates a bracket of values. For instance, $[/tex]30.0-39.9[tex]$ means all values starting from 30.0 up to, but not including 40.0.
- The relative frequency beside each range tells us the fraction of the total data that falls into that range.
4. List of Relative Frequencies:
- Below are the relative frequencies for each specified price range:
- $[/tex]30.0-39.9[tex]$: 0.056
- $[/tex]40.0-49.9[tex]$: 0.222
- $[/tex]50.0-59.9[tex]$: 0.333
- $[/tex]60.0-69.9[tex]$: 0.111
- $[/tex]70.0-79.9[tex]$: 0.083
- $[/tex]80.0-89.9[tex]$: 0.083
- $[/tex]90.0-99.9[tex]$: 0.028
- $[/tex]100.0-109.9[tex]$: 0.056
- $[/tex]110.0-119.9[tex]$: 0.000
- $[/tex]120.0-129.9[tex]$: 0.000
- $[/tex]130.0-139.9[tex]$: 0.000
- $[/tex]140.0-149.9[tex]$: 0.000
- $[/tex]150.0-159.9[tex]$: 0.028
5. Analysis of the Data:
- The highest relative frequency is 0.333 for the $[/tex]50.0-59.9[tex]$ range, indicating that this price range contains the largest proportion of data points relative to others.
- Several ranges have a relative frequency of 0.000, indicating that no data points fall within those ranges (like $[/tex]110.0-119.9[tex]$ to $[/tex]140.0-149.9$).
- Understanding the least and most frequent categories can be important in various real-world scenarios, such as market analysis or pricing strategies.
This approach allows us to understand the distribution of data across different price ranges using relative frequency, helping to identify trends or patterns in the data set.
### Step-by-Step Solution
1. Understanding Relative Frequency:
- Relative frequency is a measure that tells us the proportion of data points that fall within a particular interval or category out of the total number of data points. It's often expressed as a decimal or percentage.
2. Given Table:
- We have a table listing price ranges (in \[tex]$1000s) alongside their respective relative frequencies.
3. Interpreting the Table:
- Each price range indicates a bracket of values. For instance, $[/tex]30.0-39.9[tex]$ means all values starting from 30.0 up to, but not including 40.0.
- The relative frequency beside each range tells us the fraction of the total data that falls into that range.
4. List of Relative Frequencies:
- Below are the relative frequencies for each specified price range:
- $[/tex]30.0-39.9[tex]$: 0.056
- $[/tex]40.0-49.9[tex]$: 0.222
- $[/tex]50.0-59.9[tex]$: 0.333
- $[/tex]60.0-69.9[tex]$: 0.111
- $[/tex]70.0-79.9[tex]$: 0.083
- $[/tex]80.0-89.9[tex]$: 0.083
- $[/tex]90.0-99.9[tex]$: 0.028
- $[/tex]100.0-109.9[tex]$: 0.056
- $[/tex]110.0-119.9[tex]$: 0.000
- $[/tex]120.0-129.9[tex]$: 0.000
- $[/tex]130.0-139.9[tex]$: 0.000
- $[/tex]140.0-149.9[tex]$: 0.000
- $[/tex]150.0-159.9[tex]$: 0.028
5. Analysis of the Data:
- The highest relative frequency is 0.333 for the $[/tex]50.0-59.9[tex]$ range, indicating that this price range contains the largest proportion of data points relative to others.
- Several ranges have a relative frequency of 0.000, indicating that no data points fall within those ranges (like $[/tex]110.0-119.9[tex]$ to $[/tex]140.0-149.9$).
- Understanding the least and most frequent categories can be important in various real-world scenarios, such as market analysis or pricing strategies.
This approach allows us to understand the distribution of data across different price ranges using relative frequency, helping to identify trends or patterns in the data set.
