Answer :
Sure! Let's go through the solution for the given problem step-by-step:
We have a list of train fares and need to find the percentile ranks for specific fares. Here is the list of fares from which we need to make our calculations:
```
49, 88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 284
49, 88, 88, 88, 119, 133, 133, 161, 161, 173, 173, 173, 173, 272, 284
88, 88, 88, 119, 119, 133, 133, 161, 161, 173, 173, 173, 272, 272, 284
88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 272, 284
88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 284, 284
88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 284, 284
```
### Part (a): Find the percentile rank for a fare of [tex]$119
1. Count the number of fares less than or equal to $[/tex]119:
- There are [tex]\(27\)[/tex] fares that are less than or equal to [tex]$119.
2. Total number of fares:
- There are \(90\) total fares.
3. Calculate the percentile rank:
- The percentile rank is calculated using the formula:
\( \text{Percentile Rank} = \left(\frac{\text{Number of Fares} \leq 119}{\text{Total Number of Fares}}\right) \times 100 \)
- Plugging in the numbers:
\( \text{Percentile Rank} = \left(\frac{27}{90}\right) \times 100 = 30.00 \)
So, the percentile rank for a fare of $[/tex]119 is 30.00%.
### Part (b): Find the percentile rank for a fare of [tex]$272
1. Count the number of fares less than or equal to $[/tex]272:
- There are [tex]\(82\)[/tex] fares that are less than or equal to [tex]$272.
2. Total number of fares:
- There are still \(90\) total fares.
3. Calculate the percentile rank:
- The percentile rank is calculated using the formula:
\( \text{Percentile Rank} = \left(\frac{\text{Number of Fares} \leq 272}{\text{Total Number of Fares}}\right) \times 100 \)
- Plugging in the numbers:
\( \text{Percentile Rank} = \left(\frac{82}{90}\right) \times 100 = 91.11 \)
So, the percentile rank for a fare of $[/tex]272 is 91.11%.
### Part (c): Based on your first two answers, which train fare would have a percentile rank of approximately 82%?
Given the data we have analyzed, the fare which has a percentile rank of approximately 82% is [tex]$173.
In summary:
a. The percentile rank for a fare of $[/tex]119 is 30.00%.
b. The percentile rank for a fare of [tex]$272 is 91.11%.
c. The fare of approximately 82% percentile rank is $[/tex]173.
We have a list of train fares and need to find the percentile ranks for specific fares. Here is the list of fares from which we need to make our calculations:
```
49, 88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 284
49, 88, 88, 88, 119, 133, 133, 161, 161, 173, 173, 173, 173, 272, 284
88, 88, 88, 119, 119, 133, 133, 161, 161, 173, 173, 173, 272, 272, 284
88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 272, 284
88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 284, 284
88, 88, 88, 119, 133, 133, 133, 161, 171, 173, 173, 173, 272, 284, 284
```
### Part (a): Find the percentile rank for a fare of [tex]$119
1. Count the number of fares less than or equal to $[/tex]119:
- There are [tex]\(27\)[/tex] fares that are less than or equal to [tex]$119.
2. Total number of fares:
- There are \(90\) total fares.
3. Calculate the percentile rank:
- The percentile rank is calculated using the formula:
\( \text{Percentile Rank} = \left(\frac{\text{Number of Fares} \leq 119}{\text{Total Number of Fares}}\right) \times 100 \)
- Plugging in the numbers:
\( \text{Percentile Rank} = \left(\frac{27}{90}\right) \times 100 = 30.00 \)
So, the percentile rank for a fare of $[/tex]119 is 30.00%.
### Part (b): Find the percentile rank for a fare of [tex]$272
1. Count the number of fares less than or equal to $[/tex]272:
- There are [tex]\(82\)[/tex] fares that are less than or equal to [tex]$272.
2. Total number of fares:
- There are still \(90\) total fares.
3. Calculate the percentile rank:
- The percentile rank is calculated using the formula:
\( \text{Percentile Rank} = \left(\frac{\text{Number of Fares} \leq 272}{\text{Total Number of Fares}}\right) \times 100 \)
- Plugging in the numbers:
\( \text{Percentile Rank} = \left(\frac{82}{90}\right) \times 100 = 91.11 \)
So, the percentile rank for a fare of $[/tex]272 is 91.11%.
### Part (c): Based on your first two answers, which train fare would have a percentile rank of approximately 82%?
Given the data we have analyzed, the fare which has a percentile rank of approximately 82% is [tex]$173.
In summary:
a. The percentile rank for a fare of $[/tex]119 is 30.00%.
b. The percentile rank for a fare of [tex]$272 is 91.11%.
c. The fare of approximately 82% percentile rank is $[/tex]173.
