Maths statistics and probability questions:

1. In statistics, what is the formula for calculating the mean of a set of numbers?
a) Sum of all numbers / Total number of numbers
b) Highest number - Lowest number
c) Median of the numbers
d) Mode of the numbers

2. What is the range of the following set of numbers: 12, 15, 18, 21, 24?
a) 9
b) 12
c) 15
d) 18

3. In probability, what is the formula for calculating the probability of an event A occurring?
a) P(A) = Number of favorable outcomes / Total number of outcomes
b) P(A) = Total number of outcomes / Number of favorable outcomes
c) P(A) = Number of favorable outcomes * Total number of outcomes
d) P(A) = Total number of outcomes - Number of favorable outcomes

4. If the probability of event A occurring is 0.4 and the probability of event B occurring is 0.3, what is the probability of both events A and B occurring?
a) 0.7
b) 0.6
c) 0.5
d) 0.4

5. In statistics, which measure of central tendency is most affected by outliers in a dataset?
a) Mean
b) Median
c) Mode
d) Range

6. What is the standard deviation of the following set of numbers: 10, 12, 14, 16, 18?
a) 2
b) 3
c) 4
d) 5

7. In probability, what is the complement of an event A?
a) The event A itself
b) The opposite of event A not occurring
c) The probability of event A occurring
d) The sum of all possible outcomes

8. If the probability of event A occurring is 0.6 and the probability of event B occurring is 0.7, what is the probability of either event A or event B occurring?
a) 0.13
b) 0.6
c) 0.7
d) 0.8

9. In statistics, what does the term "correlation coefficient" measure?
a) The strength and direction of a linear relationship between two variables
b) The average value in a dataset
c) The spread of data points around the mean
d) The most frequently occurring value in a dataset

10. What is the interquartile range (IQR) of the following set of numbers: 5, 8, 10, 12, 15, 20?
a) 10
b) 12
c) 13
d) 15

11. In probability, what is the formula for calculating the conditional probability of event A given that event B has occurred?
a) P(A|B) = P(A and B) / P(B)
b) P(A|B) = P(A and B) * P(B)
c) P(A|B) = P(B|A) * P(A)
d) P(A|B) = P(A and B) + P(B)

12. If the mean of a dataset is 25 and the standard deviation is 5, what percentage of data points fall within one standard deviation from the mean?
a) 34%
b) 68%
c) 95%
d) 99%

13. In statistics, what does a box plot display about a dataset?
a) The spread and skewness of data points
b) The mean and median values
c) The range and standard deviation
d) The mode and variance

14. What is the probability of rolling a prime number (2, 3, or 5) on a fair six-sided die?
a) 1/2
b) 1/3
c) 1/4
d) 1/6

15. In statistics, if a dataset has a skewness value of -0.5, what type of skewness does it exhibit?
a) Positively skewed
b) Negatively skewed
c) Symmetrically distributed
d) No skewness

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What is the domain of f(x) = sgn(-x) ?
A. Negative real numbers
B. {-1, 0, 1}
C. An element of real numbers
D. An element of intigers

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