https://file.aiquickdraw.com/mathbot/file/172438394665121ot98lf.jpg

a. Find the percentile rank for a fare of $119.
b. Find the percentile rank for a fare of $272.
c. Based on your first two answers, which train fare would have a percentile rank of approximately 82%?

Let's analyze the data from the image to answer the questions. I'll examine the list of train fares and then calculate the percentile ranks for the given values.

### Extracting the Data

From the image, the list of fares is:

```
0, 0, 0, 0, 0, 0, 0, 49, 88, 88, 88, 88, 88, 88, 88, 98, 98, 98, 119, 119, 133, 133, 153, 161, 161, 161, 173, 173, 173, 272, 272, 284
```

This list has 32 fares.

### Part a: Percentile Rank for a Fare of $119

To find the percentile rank for a fare of $119:
1. Count the number of fares less than $119.
2. Count the number of fares equal to $119.
3. Use the formula for percentile rank:

\[
\text{Percentile Rank} = \frac{L + 0.5E}{N} \times 100
\]

where:
- $L$ is the number of fares less than $119.
- $E$ is the number of fares equal to $119.
- $N$ is the total number of fares.

### Part b: Percentile Rank for a Fare of $272

We will use the same formula and steps as above for $272.

### Part c: Train Fare with Approximately 82% Percentile Rank

We need to find a fare where the calculated percentile rank is approximately 82%.

Let's calculate each step.Here are the results:

a. **Percentile rank for a fare of $119**: 59.375%.  
b. **Percentile rank for a fare of $272**: 93.75%.  
c. **Train fare with a percentile rank of approximately 82%**: Based on the calculations, there is no exact fare in the list that corresponds to an 82% percentile rank. This means the closest percentile ranks fall either below or above 82%.

If you have any more questions or need further clarification, feel free to ask!

### Additional Questions:
1. How do you calculate percentile ranks when values are not exactly present?
2. What is the difference between percentile and percentile rank?
3. How can we interpret percentile rank in a real-world scenario?
4. How does the percentile rank change with different data distributions?
5. Can we use different methods to approximate the 82% rank?

**Tip:** Understanding the percentile rank can help you determine the relative standing of a value within a data set, which is useful in statistics and decision-making.

Learn how to calculate percentile ranks for train fares of $119 and $272 using statistical methods. Understand the concept of percentile rank and its application in analyzing data distributions. Suitable for high school students and anyone interested in statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation