Answer :
Sure! Let's go through the problem step-by-step to understand how we find the percentile rank for specific train fares and identify a fare that corresponds to an approximate percentile rank of 82%.
a. Find the percentile rank for a fare of [tex]$119:
1. Arrange the Data:
The first step in finding the percentile rank of a fare is to ensure we have all the fare data in order, from the smallest to the largest value. This is done to easily identify the position of each fare within the data set.
2. Count the Total Number of Fares:
Count how many fares are in the list. In this case, there are 90 fares.
3. Determine Position:
Identify the position of the fare $[/tex]119 in the ordered list. Remember, the position is based on counting starting from the smallest value.
4. Calculate Percentile Rank:
Use the formula for percentile rank:
[tex]\[
\text{Percentile Rank} = \frac{\text{Position of the fare $119$}}{\text{Total number of fares}} \times 100
\][/tex]
5. Result:
For the fare of [tex]$119, the percentile rank is approximately 23.33%.
b. Find the percentile rank for a fare of $[/tex]272:
1. Determine Position:
Find where the fare [tex]$272 is positioned in the ordered list.
2. Calculate Percentile Rank:
Again, use the same formula:
\[
\text{Percentile Rank} = \frac{\text{Position of the fare $[/tex]272[tex]$}}{\text{Total number of fares}} \times 100
\]
3. Result:
For the fare of $[/tex]272, the percentile rank is approximately 83.33%.
c. Identify the fare with a percentile rank of approximately 82%:
1. Approximate Position:
To find which fare corresponds to approximately an 82nd percentile, you calculate the position as follows:
[tex]\[
\text{Position} = 0.82 \times \text{Total number of fares}
\][/tex]
2. Select the Fare:
Find the fare that is at or near this calculated position in the ordered list.
3. Result:
The fare with a percentile rank of approximately 82% is [tex]$173.
In summary:
- The percentile rank for a fare of $[/tex]119 is about 23.33%.
- The percentile rank for a fare of [tex]$272 is about 83.33%.
- A fare of $[/tex]173 corresponds to a percentile rank of approximately 82%.
a. Find the percentile rank for a fare of [tex]$119:
1. Arrange the Data:
The first step in finding the percentile rank of a fare is to ensure we have all the fare data in order, from the smallest to the largest value. This is done to easily identify the position of each fare within the data set.
2. Count the Total Number of Fares:
Count how many fares are in the list. In this case, there are 90 fares.
3. Determine Position:
Identify the position of the fare $[/tex]119 in the ordered list. Remember, the position is based on counting starting from the smallest value.
4. Calculate Percentile Rank:
Use the formula for percentile rank:
[tex]\[
\text{Percentile Rank} = \frac{\text{Position of the fare $119$}}{\text{Total number of fares}} \times 100
\][/tex]
5. Result:
For the fare of [tex]$119, the percentile rank is approximately 23.33%.
b. Find the percentile rank for a fare of $[/tex]272:
1. Determine Position:
Find where the fare [tex]$272 is positioned in the ordered list.
2. Calculate Percentile Rank:
Again, use the same formula:
\[
\text{Percentile Rank} = \frac{\text{Position of the fare $[/tex]272[tex]$}}{\text{Total number of fares}} \times 100
\]
3. Result:
For the fare of $[/tex]272, the percentile rank is approximately 83.33%.
c. Identify the fare with a percentile rank of approximately 82%:
1. Approximate Position:
To find which fare corresponds to approximately an 82nd percentile, you calculate the position as follows:
[tex]\[
\text{Position} = 0.82 \times \text{Total number of fares}
\][/tex]
2. Select the Fare:
Find the fare that is at or near this calculated position in the ordered list.
3. Result:
The fare with a percentile rank of approximately 82% is [tex]$173.
In summary:
- The percentile rank for a fare of $[/tex]119 is about 23.33%.
- The percentile rank for a fare of [tex]$272 is about 83.33%.
- A fare of $[/tex]173 corresponds to a percentile rank of approximately 82%.
