Math / Data & Statistics

QuestionIn one math class, the first exam had an average score of $80.7 \%$ with a standard deviation of $12.1 \%$ . The second exam had a mean score of $78.8 \%$ , with a standard deviation of $20.8 \%$ .
Based on these numbers, tell whether each statement is true or false.
Part: $0 / 6$
Part 1 of 6 (a) Most students did better on the second exam.
The statement is (Choose one) $\nabla$ .

Studdy Solution

STEP 1

1. The average score (mean) and standard deviation of both exams are known.
2. "Most students did better" implies comparing the distribution of scores around the mean for each exam.

STEP 2

1. Understand the relationship between mean and standard deviation.
2. Analyze the spread of scores for each exam.
3. Determine if most students did better on the second exam.

STEP 3

Understand that the mean represents the average score, while the standard deviation indicates the spread of scores around the mean. A smaller standard deviation means scores are closer to the mean, while a larger standard deviation means scores are more spread out.

STEP 4

Compare the means and standard deviations of both exams:
- First exam: Mean = $80.7\%$ , Standard deviation = $12.1\%$ . - Second exam: Mean = $78.8\%$ , Standard deviation = $20.8\%$ .

STEP 5

Analyze the implications: - The first exam has a higher mean, suggesting that on average, students scored higher on the first exam. - The second exam has a larger standard deviation, indicating a wider spread of scores, meaning more variability in student performance.

STEP 6

Conclude whether most students did better on the second exam: - Since the mean score is lower on the second exam and the variability is higher, it is unlikely that most students did better on the second exam.
The statement is:
$\text{False}$

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Studdy Solution

STEP 1

1. The average score (mean) and standard deviation of both exams are known.
2. "Most students did better" implies comparing the distribution of scores around the mean for each exam.

STEP 2

1. Understand the relationship between mean and standard deviation.
2. Analyze the spread of scores for each exam.
3. Determine if most students did better on the second exam.

STEP 3

Understand that the mean represents the average score, while the standard deviation indicates the spread of scores around the mean. A smaller standard deviation means scores are closer to the mean, while a larger standard deviation means scores are more spread out.

STEP 4

Compare the means and standard deviations of both exams:
- First exam: Mean = $80.7\%$ , Standard deviation = $12.1\%$ . - Second exam: Mean = $78.8\%$ , Standard deviation = $20.8\%$ .

STEP 5

Analyze the implications: - The first exam has a higher mean, suggesting that on average, students scored higher on the first exam. - The second exam has a larger standard deviation, indicating a wider spread of scores, meaning more variability in student performance.

STEP 6

Conclude whether most students did better on the second exam: - Since the mean score is lower on the second exam and the variability is higher, it is unlikely that most students did better on the second exam.
The statement is:
$\text{False}$

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Studdy Solution

STEP 1

1. The average score (mean) and standard deviation of both exams are known.2. "Most students did better" implies comparing the distribution of scores around the mean for each exam.

STEP 2

1. Understand the relationship between mean and standard deviation.2. Analyze the spread of scores for each exam.3. Determine if most students did better on the second exam.

STEP 3

Understand that the mean represents the average score, while the standard deviation indicates the spread of scores around the mean. A smaller standard deviation means scores are closer to the mean, while a larger standard deviation means scores are more spread out.

STEP 4

Compare the means and standard deviations of both exams:- First exam: Mean = 80.7%80.7\%80.7%, Standard deviation = 12.1%12.1\%12.1%. - Second exam: Mean = 78.8%78.8\%78.8%, Standard deviation = 20.8%20.8\%20.8%.

STEP 5

Analyze the implications: - The first exam has a higher mean, suggesting that on average, students scored higher on the first exam. - The second exam has a larger standard deviation, indicating a wider spread of scores, meaning more variability in student performance.

STEP 6

Conclude whether most students did better on the second exam: - Since the mean score is lower on the second exam and the variability is higher, it is unlikely that most students did better on the second exam.The statement is:False \text{False} False

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. The average score (mean) and standard deviation of both exams are known.
2. "Most students did better" implies comparing the distribution of scores around the mean for each exam.

1. Understand the relationship between mean and standard deviation.
2. Analyze the spread of scores for each exam.
3. Determine if most students did better on the second exam.

Compare the means and standard deviations of both exams:
- First exam: Mean = $80.7\%$ , Standard deviation = $12.1\%$ . - Second exam: Mean = $78.8\%$ , Standard deviation = $20.8\%$ .

Conclude whether most students did better on the second exam: - Since the mean score is lower on the second exam and the variability is higher, it is unlikely that most students did better on the second exam.
The statement is:
$\text{False}$