Statistics and Probability MCQs | STA301 MCQs | Set 8
Statistics and Probability MCQs | STA301 MCQs | Set 8
MCQs (Multiple Choice Questions)
1) Which is the appropriate average for finding the average speed of a car:
a) Mean
b) Geometric mean
c) Harmonic mean
d) Weighted mean
Correct Answer:
The correct answer is 'c'.
Explanation:
Average speed can be determined by dividing the total distance by the total time, which is the harmonic mean of the speeds.
The harmonic mean is a measure of central tendency that is used when the average of rates is required.
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2) What will be the value of the total amount of dispersion obtained by summing the `(X-\barX)` ?
a) 0
b) -1
c) 1
d) 100
Correct Answer:
The correct answer is 'a'.
Explanation:
In the expression `(X - \barX)`, (X) represents individual values in a dataset, and `(\barX )` represents the mean (average) of the dataset.
When we calculate `(X - \barX)` for each value and sum them up, the positive deviations from the mean will cancel out the negative deviations, resulting in a total sum of 0.
This is because the sum of deviations above the mean is equal to the sum of deviations below the mean. So, when we sum up the deviations (`(X - \barX)`, the positive and negative values balance each other out, yielding a total amount of dispersion of 0.
Therefore, the value of the total amount of dispersion obtained by summing `(X - \barX)` is 0.
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3) The deviation of a distribution from symmetry is called:
a) Kurtosis
b) Skewness
c) Dispersion
d) Flatness
Correct Answer:
The correct answer is 'b'.
Explanation:
Skewness is a statistical measure that describes the asymmetry of a
probability distribution or data set. When a distribution is symmetric, it
means that its left and right sides are mirror images of each other.
Skewness measures how much the distribution deviates from this
symmetry.
In other words, if a distribution is skewed, it means that it's not evenly balanced around its central point. If the tail on the right side of the distribution (the positive side) is longer than the left tail, it's called positively skewed or right-skewed. On the other hand, if the left tail is longer than the right tail, it's called negatively skewed or left-skewed.
Skewness is an important concept in statistics and data analysis because it helps us understand the shape of a distribution. It gives insights into whether the distribution is concentrated more towards one side or if it's spread out in a certain direction. This information can be useful for making informed decisions and interpretations when analyzing data.
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4) For the independent events A and B if P(A) = 0.25, P(B) = 0.40 then P(A `\cap` B) = _______
a) 0.65
b) 0.1
c) 0.50
d) 0.15
Correct Answer:
The correct answer is 'b'.
Explanation:
The probability of the independent events A and B both occurring, denoted as P(A ∩ B), can be calculated by multiplying the probabilities of each event:
P(A ∩ B) = P(A) * P(B)
Given that P(A) = 0.25 and P(B) = 0.40:
P(A ∩ B) = 0.25 * 0.40 = 0.10
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5) The variable plotted on the vertical or Y-axis in a scatter diagram is called the:
a) Scatter Variable
b) Independent Variable
c) Dependent Variable
d) Correlation Variable
Correct Answer:
The correct answer is 'c'.
Explanation:
In a scatter diagram or scatter plot, two variables are plotted against each other to explore the relationship between them. These variables are often referred to as the independent variable and the dependent variable.
The independent variable is the variable that you control or manipulate in an experiment or study. It's the variable that you believe might have an effect on another variable. It is typically plotted on the horizontal or X-axis.
The dependent variable is the variable that you measure or observe in response to changes in the independent variable. It's the outcome or result that you're interested in studying. It is usually plotted on the vertical or Y-axis.
For example, let's consider a study where you're investigating the
relationship between the amount of studying (independent variable)
and exam scores (dependent variable). In a scatter plot, you would
plot the amount of studying on the X-axis and the exam scores on
the Y-axis. The exam scores depend on how much studying was done,
making them the
dependent variable in this case.
So, in summary, the dependent variable is the one that you're trying to understand or predict based on changes in the independent variable, and it's plotted on the Y-axis in a scatter diagram.
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6) The level of satisfaction for a certain facility which Govt. is providing is the example of:
a) Constant
b) Qualitative variable
c) Variable
d) Quantitative
Correct Answer:
The correct answer is 'b'.
Explanation:
A qualitative variable, also known as a categorical variable, is a type of variable that represents categories or labels. It describes qualities or characteristics that cannot be measured in numerical terms. Qualitative variables are typically non-numeric and can be divided into different categories or groups.
In the context of your question, the "level of satisfaction" for a
facility provided by the government is not something that can
be directly measured with numbers. Instead, it falls into
different categories that describe the degree of satisfaction.
These categories
might include labels like "Very Satisfied," "Satisfied," "Neutral,"
"Dissatisfied," and "Very Dissatisfied."
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7) Quantitative variable is further divided into:
a) Continuous variable
b) Discrete variable
c) Continuous & Discrete variable
d) None of the above
Correct Answer:
The correct answer is 'c'.
Explanation:
Quantitative variables are variables that represent quantities and can be measured numerically. They can take on numerical values and be subjected to mathematical operations.
Quantitative variables are further divided into two main subtypes:
a) Continuous variable: A continuous variable can take on any value within a certain range. It can have infinite possible values and is often measured using real numbers. Examples of continuous variables include height, weight, time, and temperature. These variables can be measured to very precise levels, including decimal places.
b) Discrete variable: A discrete variable can only take on specific, distinct values. These values are often counted and are usually whole numbers. Examples of discrete variables include the number of people in a household, the number of cars in a parking lot, and the number of books on a shelf.
So, the correct answer is c) Continuous & Discrete variable, as quantitative variables are indeed further divided into these two subtypes.
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8) If you connect the midpoints of rectangles in a histogram by a series of lines that also touches the x-axis from both ends, what will you get?
a) Ogive
b) Frequency polygon
c) Frequency curve
d) Historigram
Correct Answer:
The correct answer is 'b'.
Explanation:
A frequency polygon is a graphical representation that displays the
distribution of a dataset. It is created by connecting the
midpoints of the tops of the rectangles (or bars) in a
histogram with straight lines. These lines form a polygon that
provides a visual
representation of how the data is distributed across different
intervals or classes.
Here's how it works:
Histogram: A histogram is a graphical representation that groups data into intervals or classes and displays the frequency (or count) of observations falling into each interval. The height of each rectangle (bar) in the histogram represents the frequency of data in that interval.
Frequency Polygon: To create a frequency polygon, you plot the midpoints of the tops of the histogram's rectangles on a graph. Then, you connect these midpoints with straight lines. The resulting figure resembles a polygon, with the lines often extending down to touch the x-axis.
Frequency polygons are useful for visualizing the shape and distribution of data. They provide a smoother representation of the data distribution compared to histograms, making it easier to observe trends and patterns. Frequency polygons are particularly useful when comparing multiple datasets, as you can overlay multiple polygons on the same graph for comparison.
So, in summary, when you connect the midpoints of rectangles in a histogram with lines that touch the x-axis, you're creating a frequency polygon.
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9) Which type of data is collected in the population census?
a) Grouped data
b) Secondary data
c) Primary data
d) Array data
Correct Answer:
The correct answer is 'c'.
Explanation:
Primary data refers to original data that is collected directly from the source for a specific purpose or research study. It is the raw information that hasn't been previously collected or published. In the context of a population census:
Population Census: A population census is an official count of all individuals within a specific geographic area. It aims to collect detailed demographic, social, economic, and other relevant information about each individual in the population. This data is used for various purposes, such as policy-making, resource allocation, and demographic analysis.
Primary Data Collection in Census: During a population census, enumerators or census takers directly gather information from individuals or households within the population. This process involves going door-to-door and conducting interviews, surveys, or questionnaires to collect data about each individual's age, gender, occupation, education, household size, income, and other relevant characteristics.
Since this data is collected directly from the individuals being studied, it is considered primary data. It's the most authentic and reliable source of information for understanding the characteristics of a population. In contrast, secondary data would be information that is already collected by someone else, such as data from previous censuses, surveys, or other sources. Primary data is fresh and specifically gathered for the purpose at hand, making it crucial for accurate analysis and decision-making.
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10) Data obtained from the Bureau of Statistics, is an example of:
a) None of these
b) Primary data
c) Secondary data
d) Qualitative data
Correct Answer:
The correct answer is 'c'.
Explanation:
Secondary data refers to data that has been collected by
someone else for a different purpose and is now being used for
a new study or analysis. This data has not been directly
collected
by the researcher conducting the current study but has been
sourced from existing records, publications, databases, or
organizations.
In the context of data obtained from the Bureau of Statistics:
Bureau of Statistics: A Bureau of Statistics or similar government agency is responsible for collecting, compiling, and publishing various types of data related to demographics, economics, social trends, and more. This data is often gathered through surveys, censuses, and other official data collection methods.
Secondary Data: When you obtain data from the Bureau of Statistics, you're using information that was initially collected by the Bureau for its own purposes, such as monitoring economic indicators, population trends, labor statistics, and so on. If you use this data for your own research or analysis, it becomes secondary data for your study. It's considered "secondary" because you didn't collect it directly yourself; you're using data collected by another entity.
In contrast, primary data would involve conducting your own surveys, interviews, or experiments to gather original information directly from the sources you're studying. Secondary data can be a valuable resource for research, as it often provides a broader context, historical trends, or insights that might not be feasible to collect directly. However, researchers should carefully evaluate the quality, reliability, and relevance of secondary data sources.
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