The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a​ "flipped" classroom. Complete parts​ (a) through​ (c) below.

Traditional

71.271.2

69.669.6

80.180.1

67.967.9

86.486.4

78.278.2

56.456.4
 
80.680.6

80.780.7

70.470.4

63.563.5

70.770.7

60.260.2

Flipped

77.077.0

72.372.3

64.264.2

71.471.4

78.978.9

90.790.7

79.479.4

76.376.3

81.581.5

70.570.5

91.191.1

77.377.3

77.477.4

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Part 1

​(a)**** Which course has more dispersion in exam scores using the range as the measure of​ dispersion?

The traditional course has a range of 

enter your response here​, 

while the​ "flipped" course has a range of 

enter your response here. 

The 

▼
 
flipped

traditional
 
course has more dispersion.

​(Type integers or decimals. Do not​ round.)Traditional	Flipped

71.2	77.0

69.6	72.3

80.1	64.2

67.9	71.4

86.4	78.9

78.2	90.7

56.4	79.4

80.6	76.3

80.7	81.5

70.4	70.5

63.5	91.1

70.7	77.3

60.2	77.4

### Part (a) - Calculating the Range for Both Courses

To calculate the range, we use the formula:

\[
\text{Range} = \text{Maximum Value} - \text{Minimum Value}
\]

#### For the Traditional Course:
Scores:  
71.2, 69.6, 80.1, 67.9, 86.4, 78.2, 56.4, 80.6, 80.7, 70.4, 63.5, 70.7, 60.2

- **Maximum value**: 86.4
- **Minimum value**: 56.4

\[
\text{Range}_{\text{Traditional}} = 86.4 - 56.4 = 30
\]

#### For the Flipped Course:
Scores:  
77.0, 72.3, 64.2, 71.4, 78.9, 90.7, 79.4, 76.3, 81.5, 70.5, 91.1, 77.3, 77.4

- **Maximum value**: 91.1
- **Minimum value**: 64.2

\[
\text{Range}_{\text{Flipped}} = 91.1 - 64.2 = 26.9
\]

#### Conclusion:
- The **Traditional course** has a range of **30**.
- The **Flipped course** has a range of **26.9**.

Since \( 30 > 26.9 \), the **Traditional course** has more dispersion in exam scores based on the range.

Would you like details on the next parts or have any questions?

### Related Questions:
1. How would the standard deviation compare between these two sets of scores?
2. How does range differ from other measures of dispersion like variance or interquartile range?
3. What are some limitations of using the range to describe data variability?
4. Can we use box plots to visualize the dispersion of these two courses? How would they look?
5. How would changing one of the extreme values affect the range for each course?

**Tip**: The range is very sensitive to extreme values (outliers), so other measures like variance or standard deviation might give a better sense of dispersion when extreme scores are present.

The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a 'flipped' classroom. Complete parts (a) through (c) below.

Traditional: 71.2, 69.6, 80.1, 67.9, 86.4, 78.2, 56.4, 80.6, 80.7, 70.4, 63.5, 70.7, 60.2
Flipped: 77.0, 72.3, 64.2, 71.4, 78.9, 90.7, 79.4, 76.3, 81.5, 70.5, 91.1, 77.3, 77.4

(a) Which course has more dispersion in exam scores using the range as the measure of dispersion?

Analyze and compare exam score dispersion in a traditional and flipped classroom setting using the range as a measure. Learn how to calculate the range for each set of scores to determine which course has more variability. Suitable for students in Grades 10-12.

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