No verified paper has been uploaded for AJKPSC-PMS Statistics Set-9 yet.
The MCQs below are drawn from the Statistics subject category.
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of 1558 MCQs
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851
If the difference between the first quartile and the median is smaller than the difference between the median and the third quartile, how is the distribution classified?
Skewness is determined by the relative distances of quartiles from the median. If (Q2 - Q1) < (Q3 - Q2), the distribution is skewed to the left, which is known as negative skewness. This indicates that the data is more spread out on the left side of the median.
852
Given the first decile (D1) is 8, the ninth decile (D9) is 12, and the fifth decile (D5) is 6, calculate the Bowley's coefficient of skewness.
Bowley's coefficient of skewness is calculated as (D9 + D1 - 2*D5) / (D9 - D1). Substituting the values: (12 + 8 - 2*6) / (12 - 8) = (20 - 12) / 4 = 8 / 4 = 2. The result is 2, which is represented in the options as ±2.
853
Given the 90th percentile is 60, the 50th percentile is 30, and the 10th percentile is 40, calculate the coefficient of skewness.
Skewness is a descriptive statistic that quantifies the asymmetry of a probability distribution about its mean. While measures of dispersion like variance or standard deviation describe the spread of data, skewness specifically indicates the direction of the tail, showing whether the distribution is skewed to the left (negative) or right (positive).
855
Which type of distribution always results in a Coefficient of Skewness equal to zero?
A symmetrical distribution is balanced on both sides of the center. Because the mean, median, and mode coincide at the center, the third central moment is zero, leading to a skewness coefficient of zero. Any deviation from this perfect balance results in a non-zero skewness value, indicating the presence of a tail.
856
Which statistical parameter's sign is used to determine whether a distribution is positively or negatively skewed?
In statistical theory, skewness measures the asymmetry of a probability distribution. The third central moment, denoted as µ3, directly determines the direction of skewness. If µ3 is greater than zero, the distribution is positively skewed (right-skewed), and if µ3 is less than zero, it is negatively skewed (left-skewed). Other parameters like β1 and β2 relate to the square of skewness and kurtosis, respectively, rather than the sign of the skewness itself.
857
For a normal distribution, if the second central moment μ2 equals σ², what is the value of the fourth central moment μ4?
In a normal distribution, the moments are defined by the distribution's parameters. The second central moment (variance) is denoted as σ². The fourth central moment, which relates to the kurtosis of the distribution, is calculated as 3σ⁴. This relationship holds because the excess kurtosis of a normal distribution is zero, meaning the fourth standardized moment is exactly 3.
858
What specific region of a distribution curve does kurtosis describe in terms of peakness?
Kurtosis is a statistical measure that describes the 'tailedness' or the sharpness of the peak of a probability distribution. It specifically measures the concentration of data around the mode (the peak of the distribution) relative to the tails. High kurtosis indicates a sharper peak and heavier tails, while low kurtosis indicates a flatter peak.
859
In a negatively skewed distribution, where are the extreme values located?
A negatively skewed distribution, also known as left-skewed, is characterized by a long tail extending toward the lower values on the left side of the number line. Consequently, the extreme values, which pull the mean below the median, are found in the left tail.
860
In statistical analysis, what specific property of a distribution does skewness primarily measure?
While skewness is often described as measuring asymmetry, in some contexts, it is categorized under measures of dispersion or shape. The provided answer 'amount of dispersion' is technically imprecise, as skewness measures asymmetry rather than spread, but it is accepted here per the source key.
