Statistics and Probability MCQs | STA301 MCQs | Set 7
Statistics and Probability MCQs | STA301 MCQs | Set 7
MCQs (Multiple Choice Questions)
1) Which of the following value could not represent a coefficient of correlation?
a) r = 0.99
b) r = 1.09
c) r = -0.73
d) r = -1
Correct Answer:
The correct answer is 'b'.
Explanation:
In correlation analysis, the coefficient of correlation, denoted by 'r', measures the strength and direction of the relationship between two variables. The coefficient of correlation ranges between -1 and +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.
Therefore, the value that could not represent a coefficient of correlation is r = 1.09. The coefficient of correlation cannot exceed +1 or -1, so a value of 1.09 is outside the valid range for a correlation coefficient.
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2) The condition probability is P(A|B) is given by formula:
a) `{P(A\cupB)}/{P(A)}`
b) `{P(A\capB)}/{P(B)}`
c) `{P(A\capB)}/{P(A)}`
d) `{P(A\cupB)}/{P(B)}`
Correct Answer:
The correct answer is 'b'.
Explanation:
The correct formula for conditional probability, denoted as P(A|B), is `{P(A∩B)}/{P(B)}`.
In this formula:
P(A∩B) represents the probability of the intersection of events A and B, i.e., the probability that both events A and B occur simultaneously.
P(B) represents the probability of event B occurring.
To calculate the conditional probability of event A given that event B has occurred, we divide the probability of the intersection of A and B by the probability of event B.
So, the correct formula for conditional probability is `{P(A∩B)}/{P(B)}`.
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3) If a curve has a longer tail to the right, it is called:
a) Positively skewed
b) Negatively skewed
c) J-shaped
d) Symmetric
Correct Answer:
The correct answer is 'a'.
Explanation:
Skewness refers to the asymmetry of a probability distribution or a data set. In a positively skewed distribution, also known as right-skewed distribution, the tail of the distribution extends towards the right side, indicating that there are few extreme values on the right side. The majority of the data is concentrated on the left side of the distribution, while the right tail is longer.
Therefore, when a curve has a longer tail to the right, it is referred to as positively skewed.
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4) A set that contains all possible outcomes of a system is known as
a) Finite Set
b) Infinite Set
c) Universal Set
d) None of these
Correct Answer:
The correct answer is 'c'.
Explanation:
The universal set, also called the sample space, is a concept in set theory that represents the collection of all possible elements or outcomes in a particular context or problem. It encompasses every possible outcome or element that can be observed or considered within that specific system or context.
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5) Mean is affected by the change of:
a) Origin Only
b) Scale Only
c) Origin and Scale
d) Not affected
Correct Answer:
The correct answer is 'c'.
Explanation:
The mean is a measure of central tendency that represents the average value of a dataset. It is calculated by summing all the values in the dataset and dividing it by the total number of observations.
When the origin (i.e., the point of reference or the starting point) or the scale (i.e., the units of measurement) of the dataset is changed, the values within the dataset also change. Consequently, the sum of the values and the total number of observations used in the calculation of the mean are affected.
Thus, any change in the origin or scale of the dataset will lead to a change in the mean. Therefore, the mean is affected by the change of origin and scale.
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6) What will be the mode for the data 2, 3, 4, 5, 4, 6, 4?
a) 2
b) 3
c) 4
d) 5
Correct Answer:
The correct answer is 'c'.
Explanation:
The mode is the value that appears most frequently in a dataset. In this case, the number 4 appears three times, which is more frequently than any other number in the set. Therefore, the mode for the given data is 4.
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7) It is easy to find the median when data is ...........
a) Arranged
b) Discrete
c) Attributed
d) Continuous
Correct Answer:
The correct answer is 'a'.
Explanation:
The median is a measure of central tendency that represents the middle value in a dataset. When the data is arranged in ascending or descending order, finding the median becomes straightforward.
By arranging the data, you can easily identify the middle value. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
Therefore, when the data is arranged, it is easier to find the median.
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8) A letter is chosen at random from the word STATISTICS. The probability of getting a vowel is:
a) 3/10
b) 4/10
c) 5/10
d) 6/10
Correct Answer:
The correct answer is 'a'.
Explanation:
The word "STATISTICS" contains 3 vowels (A, I, I) and 8 letters in total.
Since there are 3 vowels out of 10 letters, the probability of selecting a vowel is the ratio of the number of favorable outcomes (3 vowels) to the total number of possible outcomes (10 letters).
Hence, the probability of getting a vowel is 3/10.
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9) In a set of 20 values all the values are 2, what will be the Geometric Mean?
a) 2
b) 5
c) 10
d) 20
Correct Answer:
The correct answer is 'a'.
Explanation:
To calculate the geometric mean, we need to multiply all the values together and then take the nth root, where n is the total number of values.
In this case, we have a set of 20 values, and all the values are 2. So, we need to calculate the geometric mean of the repeated value 2, repeated 20 times.
The geometric mean can be calculated as follows:
Geometric Mean = √(2^20)
Since 2 raised to the power of 20 is 2 * 2 * 2 * ... * 2 (20
times), the geometric mean is 2.
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10) Which of the following measure of dispersion is least affected by the extreme values in a data?
a) Range
b) Quartile deviation
c) Mean absolute deviation
d) Standard deviation
Correct Answer:
The correct answer is 'a'.
Explanation:
The quartile deviation is a measure of dispersion that calculates the spread of the middle 50% of the data. It is based on the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1). The quartile deviation is calculated as (Q3 - Q1) / 2.
Unlike the range, mean absolute deviation, and standard deviation, which consider all the values in the data set, the quartile deviation focuses only on the spread of the middle 50% of the data. This makes it less sensitive to extreme values or outliers that may exist in the data set.
Therefore, the quartile deviation is the measure of dispersion that is least affected by extreme values in a data set.
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