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The MCQs below are drawn from the Statistics subject category.
Showing 1071–1080
of 1558 MCQs
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1071
Determine the weighted average contribution per unit for three products: A (6 contribution, 120 units), B (8 contribution, 100 units), and C (10 contribution, 130 units).
The weighted average is calculated by dividing the sum of the products of each value and its weight by the total sum of weights. Here, weights are the quantities: (6*120 + 8*100 + 10*130) / (120 + 100 + 130) = (720 + 800 + 1300) / 350 = 2820 / 350 ≈ 8.057. Rounding to two decimal places gives $8.06.
1072
In a perfectly symmetrical distribution where the mean is 4, what is the value of the mode?
In a perfectly symmetrical unimodal distribution, the mean, median, and mode are identical. Since the mean is given as 4, the mode must also be 4 to maintain the symmetry of the distribution.
1073
Which of the following categories are considered fundamental descriptive measures in statistics?
Descriptive statistics aim to summarize data features. Measures of central tendency (mean, median, mode) identify the center, measures of dispersion (variance, range, standard deviation) describe spread, and measures of skewness describe the asymmetry of the distribution. All three are essential components of a comprehensive descriptive analysis.
1074
Which measure of central tendency does not necessarily incorporate every individual value in a dataset into its calculation?
The median is the middle value in a sorted dataset. It only considers the position of values, not their actual numerical values. In contrast, the arithmetic mean, geometric mean, and mode all rely on the values themselves.
1075
Numerical and graphical methods are specialized procedures primarily utilized in which branch of statistics?
Descriptive statistics focuses on summarizing and presenting data using numerical measures (like mean and variance) and graphical tools (like histograms and boxplots). These methods are essential for exploring and understanding the characteristics of a dataset before performing inferential analysis.
1076
Calculate the arithmetic mean given the sum of products (Σfx) is 300, the assumed mean (A) is 35, the total number of observations (n) is 15, and the class interval width (h) is 5.
The arithmetic mean is calculated using the formula Mean = A + (Σfd/n) * h. Here, if Σfx represents the sum of deviations multiplied by frequencies (Σfd), then Mean = 35 + (300/15) * 5 = 35 + (20 * 5) = 35 + 100 = 135. This confirms the result provided in the option.
1077
For a set of 'n' values, the nth root of their product is defined as the Geometric Mean of the ______________?
The Geometric Mean is defined as the nth root of the product of n observations. It is a measure of central tendency specifically useful for data that are multiplicative in nature, such as growth rates or index numbers.
1078
What is the mathematical relationship between the mean, median, and mode for a moderately skewed distribution?
The empirical relationship between measures of central tendency in a moderately skewed distribution is defined by the formula: Mean - Mode = 3(Mean - Median). Rearranging this shows that the difference between the mean and mode is equal to three times the difference between the mean and the median.
1079
What is a desirable characteristic of a good average in terms of usability?
A good measure of central tendency should be easy to understand and interpret by the general public. Simplicity in calculation and clarity in meaning are essential criteria for a statistical measure to be effectively used in research and decision-making processes.
1080
What is the standard value assigned to the index number of the base period?
By convention, the index number for the base period is always set to 100. This provides a standardized reference point, allowing all subsequent index values to be interpreted as percentage changes relative to that base year, which simplifies the comparison of data across different time intervals.
