Q. For the data set: 5, 7, 8, 9, 10, what is the standard deviation?
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Solution
Mean = 7.5; Variance = [(5-7.5)^2 + (7-7.5)^2 + (8-7.5)^2 + (9-7.5)^2 + (10-7.5)^2] / 5 = 2; Standard Deviation = sqrt(2) = 1.41
Correct Answer: B — 2
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Q. If a card is drawn from a standard deck of 52 cards, what is the probability that it is a heart?
A.
1/4
B.
1/13
C.
1/2
D.
1/52
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Solution
There are 13 hearts in a deck of 52 cards. Therefore, the probability P(heart) = 13/52 = 1/4.
Correct Answer: A — 1/4
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Q. If a die is rolled, what is the probability of rolling a number greater than 4?
A.
1/6
B.
1/3
C.
1/2
D.
1/4
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Solution
The numbers greater than 4 on a die are 5 and 6. There are 2 favorable outcomes out of 6 total outcomes. Therefore, P(number > 4) = 2/6 = 1/3.
Correct Answer: B — 1/3
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Q. If a student guesses on a multiple-choice test with 4 options for each question, what is the probability of guessing the correct answer?
A.
1/4
B.
1/2
C.
1/3
D.
1/5
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Solution
Probability of guessing correctly = 1/4.
Correct Answer: A — 1/4
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Q. If a student guesses on a multiple-choice test with 4 options per question, what is the probability of guessing the correct answer?
A.
1/4
B.
1/2
C.
1/3
D.
1/5
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Solution
Probability of guessing correctly = 1/4.
Correct Answer: A — 1/4
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Q. If a student is selected at random from a group of 20 students, 12 of whom are boys, what is the probability that the student is a girl?
A.
1/5
B.
2/5
C.
3/5
D.
1/2
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Solution
Number of girls = 20 - 12 = 8. Probability = 8/20 = 2/5.
Correct Answer: C — 3/5
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Q. If a student is selected at random from a group of 20 students, 12 of whom are boys, what is the probability that the student is a boy?
A.
3/5
B.
2/5
C.
1/2
D.
1/3
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Solution
Probability = Number of boys / Total students = 12/20 = 3/5.
Correct Answer: A — 3/5
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Q. If a student is selected at random from a group of 20 students, 8 of whom are girls, what is the probability that the selected student is a boy?
A.
1/2
B.
3/5
C.
2/5
D.
1/5
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Solution
There are 20 - 8 = 12 boys in the group. The probability of selecting a boy is the number of boys divided by the total number of students, which is 12/20 = 3/5.
Correct Answer: B — 3/5
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Q. If a student is selected at random from a group of 20 students, where 12 are girls and 8 are boys, what is the probability that the selected student is a boy?
A.
2/5
B.
1/2
C.
3/5
D.
1/4
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Solution
The probability of selecting a boy is the number of boys divided by the total number of students, which is 8/20 = 2/5.
Correct Answer: B — 1/2
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Q. If a student is selected at random from a group of 20 students, where 8 are girls, what is the probability that the selected student is a boy?
A.
3/5
B.
1/4
C.
1/2
D.
2/5
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Solution
The number of boys is 20 - 8 = 12. The probability of selecting a boy is 12/20 = 3/5.
Correct Answer: A — 3/5
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Q. If the data set has a mean of 30 and a median of 25, what does this indicate?
A.
Data is symmetrical
B.
Data is positively skewed
C.
Data is negatively skewed
D.
Data is uniform
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Solution
Since the mean is greater than the median, the data is positively skewed.
Correct Answer: B — Data is positively skewed
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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1
Correct Answer: C — 2
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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.
Correct Answer: C — 2
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Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer: A — 4
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Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?
A.
Symmetric
B.
Positively skewed
C.
Negatively skewed
D.
Uniform
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Solution
Since the mean is greater than the median, the distribution is positively skewed.
Correct Answer: B — Positively skewed
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Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?
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Solution
Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.
Correct Answer: B — 2
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Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer: B — 4
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Q. If the data set is 1, 2, 2, 3, 4, 4, 4, 5, what is the mode?
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Solution
Mode = 4 (most frequent value).
Correct Answer: C — 4
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Q. If the data set is 4, 4, 4, 5, 5, 6, what is the mode?
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Solution
Mode = 4 (most frequent value).
Correct Answer: A — 4
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Q. If the data set is {5, 7, 7, 8, 10}, what is the mode?
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Solution
Mode = 7 (most frequently occurring value).
Correct Answer: B — 7
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Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?
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Solution
Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.
Correct Answer: B — 3
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Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?
A.
1.58
B.
2.58
C.
3.58
D.
4.58
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Solution
Mean = 7.8. Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²]/5 = 2.5. Standard Deviation = √2.5 ≈ 1.58.
Correct Answer: A — 1.58
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Q. If the data set is: 3, 7, 7, 19, what is the median?
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Solution
Median = (7 + 7) / 2 = 7.
Correct Answer: A — 7
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Q. If the data set is: 5, 7, 8, 9, 10, what is the median?
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Solution
Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.
Correct Answer: B — 8
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Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
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Solution
The standard deviation remains the same because the transformation is a shift.
Correct Answer: C — Remains the same
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Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
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Solution
Standard deviation remains the same as adding a constant does not affect dispersion.
Correct Answer: C — Remains the same
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Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?
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Solution
Q1 is the median of the first half of the data set {3, 7}, which is 7.
Correct Answer: B — 7
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Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?
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Solution
Median is the middle value, which is 8.
Correct Answer: A — 8
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Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?
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Solution
The sum of deviations from the mean is always 0.
Correct Answer: A — 0
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Q. If the following numbers are arranged in ascending order: 3, 7, 8, 12, 14, what is the range?
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Solution
Range = Maximum - Minimum = 14 - 3 = 11
Correct Answer: A — 11
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