https://file.aiquickdraw.com/mathbot/file/17270313885647yfbjc15.jpg

The image you've uploaded provides information about a data set of student test scores. It gives specific values for the quartiles, interquartile range (IQR), and defines how outliers are identified. Here is a breakdown of the key information:

### Given Information:
1. **Lower quartile (Q1)**: 24
2. **Median (Q2)**: 30
3. **Interquartile range (IQR)**: 10
4. **Upper quartile (Q3)**: (Q1 + IQR) = 24 + 10 = 34
5. **Three lowest marks**: 8, 10, 15.5
6. **Three highest marks**: 45, 52.5, 56

### Outlier Definition:
An outlier is a value that is:
- More than \( 1.5 \times \text{IQR} \) below the lower quartile.
- More than \( 1.5 \times \text{IQR} \) above the upper quartile.

The IQR is 10, so:
- \( 1.5 \times 10 = 15 \)
- Lower outlier threshold: \( Q1 - 15 = 24 - 15 = 9 \)
- Upper outlier threshold: \( Q3 + 15 = 34 + 15 = 49 \)

### Outliers:
- Any mark below 9 is an outlier: **8** is an outlier.
- Any mark above 49 is an outlier: **52.5** and **56** are outliers.

### Box Plot:
To construct the box plot, ignoring the outliers (8, 52.5, 56), you would plot:
1. **Minimum (excluding outliers)**: 10
2. **Lower quartile (Q1)**: 24
3. **Median (Q2)**: 30
4. **Upper quartile (Q3)**: 34
5. **Maximum (excluding outliers)**: 45

A box plot would have:
- The box spanning from 24 (Q1) to 34 (Q3).
- The line inside the box at 30 (the median).
- Whiskers extending from 10 (minimum, excluding outliers) to 45 (maximum, excluding outliers).
- Outliers plotted separately at 8, 52.5, and 56.

### Do you have any questions or would you like further details?

#### 5 Related Questions:
1. How would the box plot change if the outliers were included?
2. What does the interquartile range tell us about the distribution of the data?
3. How are whiskers in a box plot related to the concept of outliers?
4. Can you explain how the outliers affect the overall analysis of the data set?
5. What other methods can be used to identify outliers besides the IQR method?

#### Tip:
When analyzing data, always check for outliers as they can skew the mean and affect statistical interpretations.

A group of students took some tests. A teacher is analysing the average mark for each student. Each student obtained a different average mark. For these average marks, the lower quartile is 24, the median is 30, and the interquartile range (IQR) is 10. The three lowest average marks are 8, 10, and 15.5, and the three highest average marks are 45, 52.5, and 56. The teacher defines an outlier to be a value that is either more than 1.5 × IQR below the lower quartile or more than 1.5 × IQR above the upper quartile. The outliers have been determined to be 8, 52.5, and 56. On the grid below, draw a box plot for these data, ignoring any outliers.

Learn how to create a box plot by analyzing a group of student test scores, identifying the quartiles, interquartile range (IQR), and determining outliers. This guide explains how to calculate and plot the lower quartile, median, and upper quartile, and shows how to handle outliers using the 1.5 × IQR rule.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation