Questions: The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "Fipped" classroom. Complete parts (a) through (c) below. Traditional 69.7 69.8 79.2 67.0 84.7 78.6 56.2 81.3 81.3 72.3 64.0 69.8 60.7 Flipped 76.7 72.6 62.4 71.8 77.1 91.6 80.1 76.0 82.4 69.3 92.1 78.3 76.5 (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? The traditional course has a range of 24.5 , while the "flipped" course has a range of 29.7. The "flipped" 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 8.166, while the "flipped" course has a standard deviation of 8.161. The traditional course has more dispersion. (c) Suppose the score of 60.7 in the traditional course was incorrectly recorded as 607 . How does this affect the range? The range is now 546.8 . How does this affect the standard deviation? The standard deviation is now 148.246 . What property does this illustrate? A. Both the range and the standard deviation are resistant. B. Neither the range nor the standard deviation is resistant. C. The standard deviation is resistant, but the range is not resistant. D. The range is resistant, but the standard deviation is not resistant.

The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "Fipped" classroom. Complete parts (a) through (c) below. Traditional 69.7 69.8 79.2 67.0 84.7 78.6 56.2 81.3 81.3 72.3 64.0 69.8 60.7 Flipped 76.7 72.6 62.4 71.8 77.1 91.6 80.1 76.0 82.4 69.3 92.1 78.3 76.5 (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? The traditional course has a range of 24.5 , while the "flipped" course has a range of 29.7. The "flipped" 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 8.166, while the "flipped" course has a standard deviation of 8.161. The traditional course has more dispersion. (c) Suppose the score of 60.7 in the traditional course was incorrectly recorded as 607 . How does this affect the range? The range is now 546.8 . How does this affect the standard deviation? The standard deviation is now 148.246 . What property does this illustrate? A. Both the range and the standard deviation are resistant. B. Neither the range nor the standard deviation is resistant. C. The standard deviation is resistant, but the range is not resistant. D. The range is resistant, but the standard deviation is not resistant.
Transcript text: The following data represent exam scores in a statistics class taught using traditional lecture and a class taught using a "Fipped" classroom. Complete parts (a) through (c) below. Traditional & 69.7 & 69.8 & 79.2 & 67.0 & 84.7 & 78.6 & 56.2 & 81.3 & 81.3 & 72.3 & 64.0 & 69.8 & 60.7 & Flipped & 76.7 & 72.6 & 62.4 & 71.8 & 77.1 & 91.6 & 80.1 & 76.0 & 82.4 & 69.3 & 92.1 & 78.3 & 76.5 & (a) Which course has more dispersion in exam scores using the range as the measure of dispersion? The traditional course has a range of 24.5 , while the "flipped" course has a range of 29.7. The "flipped" 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 8.166, while the "flipped" course has a standard deviation of 8.161. The traditional course has more dispersion. (c) Suppose the score of 60.7 in the traditional course was incorrectly recorded as 607 . How does this affect the range? The range is now 546.8 . How does this affect the standard deviation? The standard deviation is now 148.246 . What property does this illustrate? A. Both the range and the standard deviation are resistant. B. Neither the range nor the standard deviation is resistant. C. The standard deviation is resistant, but the range is not resistant. D. The range is resistant, but the standard deviation is not resistant.
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Solution

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Solution Steps

Step 1: Calculate the Range

For the traditional course, the range is calculated as follows:

\[ \text{Range}_{\text{Traditional}} = \max(x_i) - \min(x_i) = 84.7 - 56.2 = 28.5 \]

For the flipped course:

\[ \text{Range}_{\text{Flipped}} = \max(x_i) - \min(x_i) = 92.1 - 62.4 \approx 29.7 \]

Step 2: Calculate the Standard Deviation

The standard deviation for the traditional course is calculated using the formula:

\[ \sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{n-1}} \]

Where \( \mu \) is the mean. The calculations yield:

\[ \text{Standard Deviation}_{\text{Traditional}} \approx 8.713 \]

For the flipped course, the standard deviation is:

\[ \text{Standard Deviation}_{\text{Flipped}} \approx 8.161 \]

Step 3: Effect of Incorrect Recording

If the score of \( 60.7 \) in the traditional course is incorrectly recorded as \( 607 \), the new range is:

\[ \text{Range}_{\text{Incorrect}} = \max(x_i) - \min(x_i) = 607 - 56.2 = 550.8 \]

The new standard deviation is calculated as:

\[ \text{Standard Deviation}_{\text{Incorrect}} \approx 148.371 \]

Step 4: Resistance of Measures

The changes in range and standard deviation illustrate that:

  • The range increased significantly due to the outlier, indicating it is not resistant.
  • The standard deviation also increased significantly, indicating it is not resistant.

Final Answer

  • The traditional course has a range of \( 28.5 \) and the flipped course has a range of approximately \( 29.7 \).
  • The traditional course has a standard deviation of approximately \( 8.713 \) and the flipped course has a standard deviation of approximately \( 8.161 \).
  • The incorrectly recorded range is \( 550.8 \) and the standard deviation is approximately \( 148.371 \).
  • The property illustrated is that neither the range nor the standard deviation is resistant.

Thus, the answer is \( \text{B} \).

\[ \boxed{\text{B}} \]

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