
The data set shows the number of homework assignments required in math classes for a month:



22

23

23

21

18

4

17

15

23

20

24

15

25

16



Which of the following statements is true based on the data set? (1 point)

There is one outlier that indicates an unusually large number of assignments required in that class.

There is one outlier that indicates an unusually small number of assignments required in that class.

There are two outliers that indicate an unusually large number of assignments required in those two classes.

There are two outliers that indicate an unusually small number of assignments required in those two classes.

To determine which of the statements is true based on the data set, we need to identify any outliers. 

1. **Data set:**  
   22, 23, 23, 21, 18, 4, 17, 15, 23, 20, 24, 15, 25, 16

2. **Find the quartiles:**
   - Arrange the data in ascending order:  
     4, 15, 15, 16, 17, 18, 20, 21, 22, 23, 23, 23, 24, 25
   - Find the median (Q2): Since there are 14 data points, the median is the average of the 7th and 8th numbers:  
     (20 + 21) / 2 = 20.5
   - Find the lower quartile (Q1): This is the median of the first half of the dataTo determine which of the statements is true based on the data set, we need to identify any outliers. 

1. **Data set:**  
   22, 23, 23, 21, 18, 4, 17, 15, 23, 20, 24, 15, 25, 16

2. **Find the quartiles:**
   - Arrange the data in ascending order:  
     4, 15, 15, 16, 17, 18, 20, 21, 22, 23, 23, 23, 24, 25
   - Find the median (Q2): Since there are 14 data points, the median is the average of the 7th and 8th numbers:  
     (20 + 21) / 2 = 20.5
   - Find the lower quartile (Q1): This is the median of the first half of the   
     15, 15, 16, 17, 18 → Median = 16
   - Find the upper quartile (Q3): This is the median of the second half of the dataTo determine which of the statements is true based on the data set, we need to identify any outliers. 

1. **Data set:**  
   22, 23, 23, 21, 18, 4, 17, 15, 23, 20, 24, 15, 25, 16

2. **Find the quartiles:**
   - Arrange the data in ascending order:  
     4, 15, 15, 16, 17, 18, 20, 21, 22, 23, 23, 23, 24, 25
   - Find the median (Q2): Since there are 14 data points, the median is the average of the 7th and 8th numbers:  
     (20 + 21) / 2 = 20.5
   - Find the lower quartile (Q1): This is the median of the first half of the   
     15, 15, 16, 17, 18 → Median = 16
   - Find the upper quartile (Q3): This is the median of the second half of the   
     22, 23, 23, 23, 24, 25 → Median = 23

3. **Calculate the interquartile range (IQR):**  
   IQR = Q3 - Q1 = 23 - 16 = 7

4. **Determine the boundaries for outliers:**  
   - Lower bound = Q1 - 1.5 × IQR = 16 - 1.5 × 7 = 16 - 10.5 = 5.5  
   - Upper bound = Q3 + 1.5 × IQR = 23 + 1.5 × 7 = 23 + 10.5 = 33.5

Any data point outside the range [5.5, 33.5] is considered an outlier.

5. **Identify outliers:**  
   The number **4** is below the lower bound of 5.5, so it is an outlier.

**Conclusion:** The statement that is true is:

**"There is one outlier that indicates an unusually small number of assignments required in that class."**

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Would you like more details or have any further questions?

Here are some relative questions:
1. How do you calculate outliers using the interquartile range?
2. What is the significance of the median in a data set?
3. How does one interpret quartiles in a data distribution?
4. Could there be outliers on both the higher and lower ends in other data sets?
5. What are other methods to detect outliers besides the IQR method?

**Tip:** Outliers can significantly affect statistical measures like the mean, so always consider how they influence data analysis.

The data set shows the number of homework assignments required in math classes for a month: 22, 23, 23, 21, 18, 4, 17, 15, 23, 20, 24, 15, 25, 16. Which of the following statements is true based on the data set?
1) There is one outlier that indicates an unusually large number of assignments required in that class.
2) There is one outlier that indicates an unusually small number of assignments required in that class.
3) There are two outliers that indicate an unusually large number of assignments required in those two classes.
4) There are two outliers that indicate an unusually small number of assignments required in those two classes.

Analyze a data set showing the number of math homework assignments over a month using the Interquartile Range (IQR) method to detect outliers. Learn how to calculate quartiles, identify the median, and determine boundaries for outliers. Suitable for students in Grades 6-8.

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