Questions: 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: 70.4, 69.4, 80.2, 66.8, 86.1, 78.8, 56.4, 80.3, 81.4, 70.9, 64.3, 70.6, 59.9 Flipped: 77.1, 72.5, 64.1, 71.4, 79.0, 92.6, 77.9, 76.3, 83.0, 70.8, 90.6, 77.9, 76.9 (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? The traditional course has a range of 29.7, while the "flipped" course has a range of 28.5. The traditional course has more dispersion. (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 8.935, while the "flipped" course has a standard deviation of 7.749. The traditional course has more dispersion. (c) Suppose the score of 59.9 in the traditional course was incorrectly recorded as 599. How does this affect the range? The range is now not provided.

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: 70.4, 69.4, 80.2, 66.8, 86.1, 78.8, 56.4, 80.3, 81.4, 70.9, 64.3, 70.6, 59.9 Flipped: 77.1, 72.5, 64.1, 71.4, 79.0, 92.6, 77.9, 76.3, 83.0, 70.8, 90.6, 77.9, 76.9 (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? The traditional course has a range of 29.7, while the "flipped" course has a range of 28.5. The traditional course has more dispersion. (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 8.935, while the "flipped" course has a standard deviation of 7.749. The traditional course has more dispersion. (c) Suppose the score of 59.9 in the traditional course was incorrectly recorded as 599. How does this affect the range? The range is now not provided.
Transcript text: 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. \begin{tabular}{llllllll} \hline Traditional & 70.4 & 69.4 & 80.2 & 66.8 & 86.1 & 78.8 & 56.4 \\ & 80.3 & 81.4 & 70.9 & 64.3 & 70.6 & 59.9 & \\ \hline Flipped & 77.1 & 72.5 & 64.1 & 71.4 & 79.0 & 92.6 & 77.9 \\ & 76.3 & 83.0 & 70.8 & 90.6 & 77.9 & 76.9 & \\ \hline \end{tabular} (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? The traditional course has a range of 29.7 , while the "flipped" course has a range of 28.5 The traditional course has more dispersion. (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 8.935 , while the "flipped" course has a standard deviation of 7.749 . The traditional course has more dispersion. (c) Suppose the score of 59.9 in the traditional course was incorrectly recorded as 599. How does this affect the range? The range is now $\square$ $\square$.
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the Range

The range is calculated as the difference between the maximum and minimum scores for each course.

For the traditional course: \[ \text{Range}_{\text{traditional}} = \max(70.4, 69.4, 80.2, 66.8, 86.1, 78.8, 56.4, 80.3, 81.4, 70.9, 64.3, 70.6, 59.9) - \min(70.4, 69.4, 80.2, 66.8, 86.1, 78.8, 56.4, 80.3, 81.4, 70.9, 64.3, 70.6, 59.9) = 86.1 - 56.4 = 29.7 \]

For the flipped course: \[ \text{Range}_{\text{flipped}} = \max(77.1, 72.5, 64.1, 71.4, 79.0, 92.6, 77.9, 76.3, 83.0, 70.8, 90.6, 77.9, 76.9) - \min(77.1, 72.5, 64.1, 71.4, 79.0, 92.6, 77.9, 76.3, 83.0, 70.8, 90.6, 77.9, 76.9) = 92.6 - 64.1 = 28.5 \]

Step 2: Calculate the Standard Deviation

The standard deviation is calculated using the formula for sample standard deviation.

For the traditional course: \[ \text{Standard Deviation}_{\text{traditional}} = \sqrt{\frac{\sum (x_i - \mu)^2}{n-1}} = 8.935 \]

For the flipped course: \[ \text{Standard Deviation}_{\text{flipped}} = \sqrt{\frac{\sum (x_i - \mu)^2}{n-1}} = 7.749 \]

Step 3: Effect of Incorrect Score on Range

If the score of \(59.9\) in the traditional course is incorrectly recorded as \(599\), the new range is calculated as follows:

\[ \text{New Range}_{\text{traditional}} = \max(70.4, 69.4, 80.2, 66.8, 86.1, 78.8, 56.4, 80.3, 81.4, 70.9, 64.3, 70.6, 599) - \min(70.4, 69.4, 80.2, 66.8, 86.1, 78.8, 56.4, 80.3, 81.4, 70.9, 64.3, 70.6, 599) = 599 - 56.4 = 542.6 \]

Final Answer

  • The traditional course has a range of \(29.7\) and the flipped course has a range of \(28.5\). The traditional course has more dispersion.
  • The standard deviation of the traditional course is \(8.935\) and the flipped course is \(7.749\). The traditional course has more dispersion.
  • The new range of the traditional course with the incorrect score is \(542.6\).

Thus, the final answers are: \[ \boxed{\text{Range (Traditional): } 29.7, \text{ Range (Flipped): } 28.5, \text{ Std Dev (Traditional): } 8.935, \text{ Std Dev (Flipped): } 7.749, \text{ New Range: } 542.6} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
What are the challenges associated with people with autism? Choose four answers. Education challenges Social isolation Mental health Employment challenges
failedAnswered
Which of the following calculations is NOT derived from the confidence interval? Choose the correct answer below. A. Difference between the limits, 2 E= (upper confidence limit) - (lower confidence limit) B. The population mean, μ= (upper confidence limit) + (lower confidence limit) C. The point estimate of μ, x̄= (upper confidence limit) + (lower confidence limit) / 2 D. The margin of error, E= (upper confidence limit) - (lower confidence limit) / 2
failedAnswered
Solve. 25 x^2+20 x+4=0 x=
failedAnswered
An atom with an electrical charge is a(n) Select one: a. isotope b. molecule c. ion d. compound
failedAnswered
Algebra II Sem 2 Apex Learning 2.3.3 Quiz: Adding and Subtracting Radicals Question 7 of 10 Which choice is equivalent to the expression below? sqrt(40) + 8 sqrt(10) + sqrt(90) A. 10 sqrt(10) B. 13 sqrt(10) C. 7 sqrt(10) D. 18 sqrt(10)