Statistics and Probability MCQs | STA301 MCQs | Set 9
Statistics and Probability MCQs | STA301 MCQs | Set 9
MCQs (Multiple Choice Questions)
1) In positively skewed distribution, which of the following relationship exists:
a) The mean, median, and mode are all equal
b) The mean is larger than the median
c) The median is larger than the mean
d) The standard deviation must be larger than the mean or the median
Correct Answer:
The correct answer is 'b'.
Explanation:
Positively skewed distributions are characterized by a tail that extends toward the higher values. This means that there are some relatively large values on the right side of the distribution that pull the mean in that direction, causing it to be larger than the median. The median, being the middle value of the dataset, is less affected by extreme values and tends to be closer to the bulk of the data.
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2) When two coins are tossed simultaneously, P (one head) is:
a) `1/4`
b) `2/4`
c) `3/4`
d) `4/4`
Correct Answer:
The correct answer is 'c'.
Explanation:
To find the probability of getting at most one head when two coins are tossed, we can consider the possible outcomes:
Two tails: This outcome has a probability of `(1/2) * (1/2) = 1/4` since each coin has a `1/2` probability of landing on tails.
One head and one tail: There are two possible ways this can occur: (head, tail) or (tail, head). Each of these outcomes has a probability of `(1/2) * (1/2) = 1/4`. So the total probability for this case is `1/4 + 1/4 = 1/2`.
Adding up the probabilities of the two favorable outcomes (getting two tails and getting one head and one tail), we get:
Probability = `1/4 + 1/2 = 3/4`.
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3) A histogram is consisting of a set of adjacent rectangles whose bases are marked off by:
a) Class Boundaries
b) Class Limits
c) Class Frequency
d) Class Marks
Correct Answer:
The correct answer is 'a'.
Explanation:
A histogram consists of a set of adjacent rectangles, where the bases of these rectangles are marked off by class boundaries. Class boundaries define the range of values that fall within each interval on the histogram. They are usually positioned midway between the class limits (upper and lower values of each interval). This helps in creating a clear representation of the data's distribution and frequency within specific intervals.
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4) The middle value of an ordered array of numbers is the
a) Mean
b) Median
c) Mode
d) Midpoint
Correct Answer:
The correct answer is 'b'.
Explanation:
The middle value of an ordered array of numbers is the median. The median
is the value that separates the dataset into two equal halves, with
half of the values being greater than the median and half being less
than the median. It is different from the mean, which is the average
of all the values, and the mode, which is the value that appears most
frequently in
the dataset.
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5) If Mean = 25 and S.D is 5 then C.V is:
a) 100%
b) 20%
c) 10%
d) 25%
Correct Answer:
The correct answer is 'b'.
Explanation:
The Coefficient of Variation (C.V.) is calculated as the ratio of
the
standard deviation (SD) to the mean (M) and is typically expressed as
a
percentage. The formula for C.V. is:
C.V. = (SD / M) * 100%
Given Mean (M) = 25 and Standard Deviation (SD) = 5:
C.V. = (5 / 25) * 100% = 20%
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6) you connect the mid-points of rectangles in a histogram by a series of lines that also touches the x-axis from both ends, you will get:
a) Ogive
b) Frequency polygon
c) Frequency curve
d) Historigram
Correct Answer:
The correct answer is 'c'.
Explanation:
When you connect the mid-points of rectangles in a histogram by a series of lines that also touch the x-axis from both ends, you obtain a frequency polygon. This graphical representation helps to visualize the distribution of data and its frequency in a more smoothed manner compared to a histogram.
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7) Serious disadvantage of using range as a measure of dispersion is that it is based on only:
a) Minimum Values
b) Maximum Values
c) Both Minimum and Maximum values
d) None of the above
Correct Answer:
The correct answer is 'c'.
Explanation:
The serious disadvantage of using the range as a measure of dispersion is that it is based on both the minimum and maximum values only. It doesn't take into account the distribution of the data points between these two extreme values, which can lead to misleading results, especially when there are outliers or when the data isn't evenly spread out within the range.
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8) Frequency of a variable is always in:
a) Fraction form
b) Percentage form
c) Less than form
d) Integer form
Correct Answer:
The correct answer is 'd'.
Explanation:
The frequency of a variable, which represents the number of times a particular value occurs in a dataset, is always expressed in integer form. Fractions and percentages are not typically used to represent frequency values, and "less than form" is not a common term in this context.
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9) `5C_5` is equal to
a) 5
b) 1
c) 10
d) 24
Correct Answer:
The correct answer is 'b'.
Explanation:
The notation "5C_5" represents a combination, also known as "n choose r," which calculates the number of ways to choose r items from a set of n items without considering the order. In this case, "5C_5" means choosing 5 items from a set of 5 items, which is essentially choosing all the items. Since there's only one way to choose all 5 items from the set of 5, the value is 1.
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10) Chebychev’s inequality does not hold for k = ?
a) 3
b) 2
c) 1
d) 0
Correct Answer:
The correct answer is 'd'.
Explanation:
Chebyshev's inequality does not hold for k = 0. Chebyshev's inequality states that for any set of data and any value k greater than 0, at least 1 - 1/k^2 of the data values will fall within k standard deviations of the mean. However, when k is equal to 0, the inequality doesn't make sense, as dividing by zero is undefined.
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