Statistics and Probability MCQs | STA301 MCQs | Set 5

Statistics and Probability MCQs | STA301 MCQs | Set 5

MCQs (Multiple Choice Questions)

1)  Which one is the formula of range:

    a)        `x_m - x_0`

    b)        `x_0 - x_m`

    c)        `{x_0 - x_m}/2`

    d)        `{x_m - x_0}/2`

Correct Answer: 

The correct answer is  'a'.

Explanation:

The formula for range, typically denoted as "R," is `x_m - x_0`.

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2)  If a player well shuffles the pack of 52 playing cards, then the probability of a black card from 52 playing cards is:

    a)        1/52

    b)        13/52

    c)         4/52

    d)        26/52

Correct Answer: 

The correct answer is  'd'.

Explanation:

A standard deck of playing cards consists of 52 cards, with 26 black cards (clubs and spades) and 26 red cards (hearts and diamonds). If the player shuffles the pack well, the probability of drawing a black card from the deck is:

Number of black cards = 26

Total number of cards = 52

Probability of drawing a black card = Number of black cards / Total number of cards

= 26 / 52

= 1/2

Therefore, the probability of drawing a black card from a well-shuffled deck of 52 playing cards is 26/52 or 1/2 or 50%. Therefore, the correct answer is the Arithmetic mean.

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3)  Pearson's coefficient of skewness is not possible if standard deviation is:

    a)        1

    b)        1.5

    c)        0

    d)        3

Correct Answer: 

The correct answer is  'c'.

Explanation:

Pearson's coefficient of skewness is not possible if the standard deviation is 0.

Pearson's coefficient of skewness measures the asymmetry of a distribution. It is calculated as:

Skewness = 3 * (Mean - Median) / Standard Deviation

If the standard deviation is 0, the denominator in the formula becomes 0, leading to an undefined result. This means that Pearson's coefficient of skewness cannot be calculated when the standard deviation is 0. 

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4) What is the difference between permutation and combination?

    a)        In permutation order is important and in combination, order is not important.

    b)        In permutation order is not important and in combination order is important.

    c)        Only combination is based on the classical definition of probability

    d)        Only permutation is based on the classical definition of probability

Correct Answer: 

The correct answer is  'a'.

Explanation:

The difference between permutation and combination is described by option
a) "In permutation, order is important, and in combination, order is not important."

Permutation:

In permutation, the order of selecting items from a set or arranging items matters. It refers to the arrangement of objects in a specific order. For example, the permutations of the letters "A," "B," and "C" would include "ABC," "ACB," "BAC," "BCA," "CAB," and "CBA." The number of permutations depends on the total number of items and the number of items selected.

Combination:

In combination, the order of selecting items from a set does not matter. It refers to the selection of objects without considering their arrangement. For example, the combinations of the letters "A," "B," and "C" would include "ABC," "ACB," "BAC," "BCA," "CAB," and "CBA," but these are all considered the same combination. The number of combinations also depends on the total number of items and the number of items selected.

Option c) and d) are not accurate. Both permutation and combination can be used in the context of probability calculations.

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5)  If data is categorized about any characteristics, then which measurement scale should be used? 

    a)        Ordinal

    b)        Interval

    c)        Nominal

    d)        Ratio

Correct Answer: 

The correct answer is  'c'.

Explanation:

Nominal scale is used when data can be categorized or classified into distinct groups or categories without any inherent order or ranking. It represents qualitative data where each category is distinct and unrelated to the others. Examples of nominal data include gender (male/female), eye color (blue/brown/green), or marital status (single/married/divorced). The categories cannot be ordered or ranked in any meaningful way.

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6) Which of the following scale has a true zero point?

    a)        Radio scale

    b)        Interval scale

    c)        Nominal scale

    d)        Ordinal scale

Correct Answer: 

The correct answer is  'a'.

Explanation:

Ratio scale is the only one among the given options that has a true zero point. In ratio scale, the zero point represents the absence of the measured attribute. It allows for ranking, ordering, and measuring the difference between values, and also provides a meaningful and absolute zero reference.

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7)  In a simple bar chart:

    a)        Width of bar is meaningful

    b)        Height of bar is meaningful

    c)        Height of bar is not meaningful

    d)        Height and width of bar are meaningful

Correct Answer: 

The correct answer is  'b'.

Explanation:

In a bar chart, the height of each bar represents the value or magnitude of the variable being represented. The taller the bar, the greater the value it represents. The height of the bar is meaningful and provides a visual comparison of the values being displayed. The width of the bar, on the other hand, is typically not meaningful in a simple bar chart. The width is usually kept constant across all bars to ensure consistent representation, and it does not convey any additional information about the data.

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8) What is the name of the following curve?

    a)        Positively skewed curve

    b)        Symmetrical curve

    c)        Symmetrical curve

    d)        Negatively skewed curve

Correct Answer: 

The correct answer is  'a'.

Explanation:

A positively skewed curve, also known as a right-skewed curve, is a term used to describe the shape of a distribution or dataset. In a positively skewed curve, the tail of the distribution extends toward the right side, while the bulk of the data is concentrated toward

the left side. 

Visually, a positively skewed curve appears as a longer or extended tail towards the right side, while the peak or mode of the distribution is closer to the left side. This indicates that there are relatively more low values or outliers on the right side of the distribution, which pulls the mean towards that direction, resulting in a long tail.

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9)  If A = {1, 2, 3, 4, 5, 10} and B = {1, 3, 5} then B`\subset`A means:

    a)        A is less than B

    b)        A is contained in B

    c)        B is contained in A

    d)        B is less than A

Correct Answer: 

The correct answer is  'c'.

Explanation:

In set theory, the symbol \subset denotes a subset relationship. When B\subsetA, it means that every element in set B is also an element of set A. In other words, B is a subset of A.

In this specific example, set B = {1, 3, 5} is indeed a subset of set A = {1, 2, 3, 4, 5, 10} because all the elements of B (1, 3, and 5) are also present in A. Thus, B is contained within

A. 

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10) The graph of cumulative frequency distribution is called:

    a)        Frequency polygon

    b)        Ogive

    c)        Frequency curve

    d)        Historigram

Correct Answer: 

The correct answer is  'b'.

Explanation:

An ogive is a graphical representation of a cumulative frequency distribution. It displays the cumulative frequency on the vertical axis and the corresponding values or intervals on the horizontal axis. The ogive is constructed by plotting points and connecting them with line segments, forming a curve that represents the cumulative frequencies.

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