Given the data set, {77, 72, 85, 66, 45, 63, 82}, identify the following values that would be used when creating the boxplot:

 

Highest 
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Upper Quartile 
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type your answer...

Median 
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type your answer...

Lower Quartile 
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type your answer...

Lowest 
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type your answer...



To construct a boxplot from the data set {77, 72, 85, 66, 45, 63, 82}, we need to identify the following values:

### Step 1: Arrange the data in ascending order.
The data set, when sorted, is:
{45, 63, 66, 72, 77, 82, 85}

### Step 2: Identify the required values.

1. **Highest (Maximum value)**:  
   The highest value in the data set is **85**.

2. **Upper Quartile (Q3)**:  
   The upper quartile is the median of the upper half of the data (above the overall median).  
   In the sorted data, the upper half is {77, 82, 85}. The median of this subset is **82**.

3. **Median**:  
   The median is the middle value of the entire data set.  
   Since there are 7 numbers, the middle value is the 4th one, which is **72**.

4. **Lower Quartile (Q1)**:  
   The lower quartile is the median of the lower half of the data (below the overall median).  
   The lower half is {45, 63, 66}, and the median of this subset is **63**.

5. **Lowest (Minimum value)**:  
   The lowest value in the data set is **45**.

### Summary of values for the boxplot:

- Highest: **85**
- Upper Quartile (Q3): **82**
- Median (Q2): **72**
- Lower Quartile (Q1): **63**
- Lowest: **45**

Would you like more details on how these values are calculated or interpreted?

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Here are 5 related questions for further understanding:
1. How is the interquartile range (IQR) calculated from this data set?
2. What would be considered an outlier in this data set based on the IQR?
3. How does a boxplot represent data distribution?
4. How would adding an additional data point affect the boxplot?
5. What are the implications of a skewed boxplot?

**Tip**: The interquartile range (IQR) is a measure of spread and is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3).

Given the data set, {77, 72, 85, 66, 45, 63, 82}, identify the following values that would be used when creating the boxplot: Highest, Upper Quartile, Median, Lower Quartile, Lowest

Learn how to create a boxplot from the data set {77, 72, 85, 66, 45, 63, 82}. This problem covers the calculation of the median, upper quartile (Q3), lower quartile (Q1), highest value, and lowest value, which are key components in boxplot creation. Suitable for students in Grades 6-8.

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