Math Problem Statement
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 71.6 68.6 80.3 67.3 84.5 77.8 56.5
81.7 81.3 71.4 63.3 69.2 59.2 Flipped 76.8 71.2 62.5 71.9 77.9 92.7 78.6 77.2 81.1 70.6 90.3 78.0 77.3 Question content area bottom 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 28.0, while the "flipped" course has a range of select: 30.2 30.2. The flipped course has more dispersion. (Type integers or decimals. Do not round.) Part 2 (b) Which course has more dispersion in exam scores using the sample standard deviation as the measure of dispersion? The traditional course has a standard deviation of enter your response here, while the "flipped" course has a standard deviation of enter your response here. The ▼ course has more dispersion. (Round to three decimal places as needed.)Traditional Flipped 71.6 76.8 68.6 71.2 80.3 62.5 67.3 71.9 84.5 77.9 77.8 92.7 56.5 78.6 81.7 77.2 81.3 81.1 71.4 70.6 63.3 90.3 69.2 78.0 59.2 77.3
Solution
Let's solve the questions step by step.
Part 1: Range as a Measure of Dispersion
The range is calculated by subtracting the smallest score from the largest score.
Traditional Course:
- Smallest score: 56.5
- Largest score: 84.5
- Range:
Flipped Course:
- Smallest score: 62.5
- Largest score: 92.7
- Range:
So, the range for the traditional course is 28.0, and the range for the flipped course is 30.2.
Answer (Part a):
The flipped course has a range of 30.2 and more dispersion.
Part 2: Standard Deviation as a Measure of Dispersion
To find the standard deviation, we will calculate it using the formula for sample standard deviation:
Where:
- is the number of scores
- are the individual scores
- is the sample mean of the scores
Traditional Course:
Scores:
- Mean (): Now, calculate the variance and standard deviation:
Flipped Course:
Scores:
- Mean (): Now, calculate the variance and standard deviation:
Answer (Part b):
- The traditional course has a standard deviation of 8.760.
- The flipped course has a standard deviation of 7.578.
- The traditional course has more dispersion based on the standard deviation.
Part 3: Relative Dispersion Conclusion
For the range, the flipped classroom had more dispersion, but for the standard deviation, the traditional classroom showed more variation.
Would you like a more detailed breakdown of the calculations or clarifications?
Here are five relative questions that expand upon this topic:
- What is the significance of using standard deviation over the range as a measure of dispersion?
- How does sample size impact the reliability of the range and standard deviation as dispersion measures?
- Can a dataset have a larger range but a smaller standard deviation? Why might this occur?
- How does the shape of the distribution (e.g., skewed, normal) affect measures of dispersion?
- What other measures of dispersion (e.g., variance, interquartile range) could we consider for these scores?
Tip: Always look at both range and standard deviation to get a clearer picture of data dispersion, as each metric highlights different aspects of the spread.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Descriptive Statistics
Measures of Dispersion
Range
Standard Deviation
Formulas
Range = Max(x) - Min(x)
Sample Standard Deviation = sqrt((1/(n-1)) * Σ(x_i - x̄)^2)
Theorems
-
Suitable Grade Level
Grades 10-12
Related Recommendation
Comparing Dispersion in Exam Scores: Traditional vs. Flipped Classroom
Comparing Exam Score Dispersion: Traditional vs. Flipped Classroom
Mean and Median Comparison in Traditional and Flipped Classrooms
Exam Score Comparison Between Traditional and Flipped Classrooms
Comparing Variability and Normality: Class A vs Class B Exam Scores