https://file.aiquickdraw.com/mathbot/file/1725502726798lsunh0tt.jpg

It looks like you've uploaded an image with a mathematical problem. Let me analyze the problem and break it down for you:

The task involves identifying outliers using the interquartile range (IQR). The summary statistics for receiving yards are provided as follows:

- **Minimum:** 20.3 yards
- **1st quartile (Q1):** 57.0 yards
- **Median:** 75.0 yards
- **3rd quartile (Q3):** 101.0 yards
- **Maximum:** 171.0 yards

### Step 1: Calculate the Interquartile Range (IQR)
The formula for IQR is:
\[
IQR = Q3 - Q1
\]
Using the provided values:
\[
IQR = 101.0 - 57.0 = 44.0 \, \text{yards}
\]

### Step 2: Calculate the outlier thresholds
To find the thresholds for identifying outliers, Ted uses the following formulas:

- **Lower Bound (Q1 - 1.5 * IQR):**
\[
Q1 - 1.5 \times IQR = 57.0 - 1.5 \times 44.0 = 57.0 - 66.0 = -9.0
\]
(After rounding to 1 decimal place: \(-9.0\))

- **Upper Bound (Q3 + 1.5 * IQR):**
\[
Q3 + 1.5 \times IQR = 101.0 + 1.5 \times 44.0 = 101.0 + 66.0 = 167.0
\]
(After rounding to 1 decimal place: \(167.0\))

### Final Answers:
- \(Q1 - 1.5 \times IQR = -9.0\)
- \(Q3 + 1.5 \times IQR = 167.0\)

These thresholds indicate that receiving yards below \(-9.0\) yards or above \(167.0\) yards would be considered outliers.

Would you like more details or have any questions about the calculation?

Here are five questions to further explore the topic:
1. What is the significance of using 1.5 times the IQR to detect outliers?
2. How does the standard deviation relate to the detection of outliers?
3. What happens if there are no values outside the calculated range for outliers?
4. Could a different multiplier (like 3 times IQR) be used for a stricter or looser definition of outliers?
5. How does the mean compare to the median, and what does it tell us about the distribution?

**Tip:** Outliers can significantly affect statistical measures like the mean. Therefore, it's important to check for them when analyzing data.

Suppose Ted is creating a football team in a video game that features many NFL players. He decides to identify players who are outliers in a few statistics he has chosen. Currently, he's looking at wide receivers. The game includes the top 100 receivers in 2015 by number of receptions. Ted, however, is more interested in receiving yards, and the table above shows the five-number summary of the available players in the game (in yards): Minimum: 20.3, 1st quartile: 57.0, Median: 75.0, 3rd quartile: 101.0, Maximum: 171.0. The mean is 78.8 with a standard deviation of 33.0. Ted first calculates the interquartile range (IQR). Next, to determine the outliers, he calculates Q1 - 1.5(IQR) and Q3 + 1.5(IQR). What are the outlier thresholds?

Learn how to calculate the interquartile range (IQR) and use it to detect outliers in NFL player statistics. Using a five-number summary of receiving yards, find out the thresholds for outliers using Q1 - 1.5(IQR) and Q3 + 1.5(IQR).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation