Statistics and Probability MCQs | STA301 MCQs | Set 4
Statistics and Probability MCQs | STA301 MCQs | Set 4
MCQs (Multiple Choice Questions )
1) The average which is defined as the reciprocal of the arithmetic mean of the reciprocals of the values is called:
a) Geometric Mean
b) Harmonic Mean
c) Mode
d) Median
Correct Answer:
The correct answer is 'b'.
Explanation:
The average that is defined as the reciprocal of the arithmetic mean of the reciprocals of the values is called the harmonic mean.
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2) An automobile is running during the first 60 Km, at the rate of 10 Km/hr. During the second 60 Km at the rate 30 Km/hr, while during the third 60 Km its speed was 40 Km/hr. What method is more appropriate to calculate the average speed?
a) Median
b) Arithmetic mean
c) Harmonic mean
d) Geometric mean
Correct Answer:
The correct answer is 'b'.
Explanation:
The most appropriate method to calculate the average speed in this scenario is the arithmetic mean.
The arithmetic mean is commonly used to calculate averages and is suitable for situations where the values being averaged are directly additive or proportional. In this case, the speeds of the automobile during the three segments are given in terms of kilometers per hour (Km/hr), which are directly additive.
To calculate the average speed, we sum up the speeds during each segment and divide by the number of segments. The arithmetic mean provides a straightforward and intuitive way to calculate the overall average speed of the automobile over the entire distance traveled.
Therefore, the correct answer is the Arithmetic mean.
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3) What is the standard deviation of the following values? 7 , 7 , 7 , 7 , 7 , 7 , 7
a) 7
b) 1
c) 49
d) 0
Correct Answer:
The correct answer is 'd'.
Explanation:
To calculate the standard deviation, we first need to find the mean (average) of the given values. In this case, the values are all the same: 7.
The formula for the standard deviation involves calculating the square root of the average of the squared differences between each value and the mean.
However, since all the values are the same and equal to 7, the differences between each value and the mean are all zero. Therefore, when we square these differences, we still get zero.
Taking the average of the squared differences results in 0, and taking the square root of 0 gives us 0. Hence, the standard deviation of the given values is 0.
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4) Which one of the following is a meso-kurtic curve?
a) Negative skewed
b) Positive skewed
c) J-shaped
d) Normal
Correct Answer:
The correct answer is 'd'.
Explanation:
The mesokurtic curve refers to a curve with medium kurtosis, which is a measure of the shape of a statistical distribution. Kurtosis indicates the degree of peakedness or flatness of a distribution compared to the normal distribution.
Among the options provided, the normal curve, represented by option d), is one that exhibits mesokurtic characteristics. The normal distribution has a kurtosis of 3, which is considered to be the baseline or reference value for kurtosis.
Negative skewed, Positive skewed, and J-shaped distributions typicall exhibit different levels of kurtosis compared to the normal distribution, indicating either more peakedness or flatness.
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5) Men tend to marry women who are slightly younger than themselves. Suppose that every man married a woman who was exactly 5 years younger than themselves. Which of the following is correct?
a) The correlation coefficient is -5.
b) The correlation coefficient is 5.
c) The correlation coefficient is 1.
d) The correlation coefficient is 0.
Correct Answer:
The correct answer is 'd'.
Explanation:
The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the variables are the ages of men and the ages of the women they marry.
If every man married a woman who was exactly 5 years younger than themselves, it implies a consistent age difference of 5 years. However, this age difference does not indicate a linear relationship that can be represented by a correlation coefficient. The correlation coefficient is used to measure the strength and direction of a linear relationship, but in this scenario, the relationship is not linear.
Therefore, the correlation coefficient between the ages of men and the ages of the women they marry would be 0, indicating no linear relationship.
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6) In a multiplication theorem P(A`\cap`B) equals:
a) P(A) P(B)
b) P(A) + P(B)
c) `P(A) \times P(B|A)`
d) `P(B|A) \times P(B)`
Correct Answer:
The correct answer is 'd'.
Explanation:
The multiplication theorem, also known as the multiplication rule, states that the probability of the intersection of two events, A and B, denoted as P(A ∩ B), is equal to the probability of event A occurring, P(A), multiplied by the conditional probability of event B occurring given that event A has occurred, P(B|A).
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7) Which one of the following is the class frequency?
a) The number of observations in each class.
b) The difference between consecutive lower-class limits
c) Always contains at least 5 observations
d) Usually a multiple of the lower limit of the first class
Correct Answer:
The correct answer is 'a'.
Explanation:
The class frequency refers to the number of observations within each class in a frequency distribution.
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8) Which of the following comes first to make frequency distribution.
a) Number of Groups
b) Class interval
c) Range
d) Tally marks
Correct Answer:
The correct answer is 'b'.
Explanation:
To create a frequency distribution, the class interval comes first. The
class interval is the range of values grouped together to form classes
or intervals. After determining the class interval, you can proceed
to calculate the frequency of values falling within each interval.
The other options mentioned, such as the number of groups, range, and
tally marks, are
determined based on the class interval and the data being analyzed.
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9) Data obtained from the Ministry of Food, is an example of:
a) Primary data
b) Secondary data
c) Qualitative data
d) None of these
Correct Answer:
The correct answer is 'b'.
Explanation:
Secondary data refers to information that has been collected by someone else or an organization for a purpose other than the current study or research. In this case, the Ministry of Food collected the data, and it is being used for a different purpose.
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10) Total angle of a Pie Chart is:
a) `90^o`
b) `180^o`
c) `270^o`
d) `360^o`
Correct Answer:
The correct answer is 'd'.
Explanation:
A pie chart represents data as a circular graph, with each category or segment represented by a slice of the circle. Since a circle has 360 degrees, the total angle of a pie chart is equal to 360 degrees. Each segment's angle is proportional to the data it represents.
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