Measures of central tendency, such as the mean, median, and mode, are designed to provide a single representative value that summarizes the center of a data distribution. These measures help researchers understand the typical value around which the data points cluster.
1062
Which measure of central tendency is most sensitive to the influence of extreme values (outliers)?
The arithmetic mean is highly sensitive to extreme values because it sums all observations and divides by the count. A single very large or very small value can significantly pull the mean toward it, unlike the median or trimmed mean, which are more robust.
1063
Which term best characterizes the arithmetic mean as a measure of central tendency?
The arithmetic mean is considered a stable measure of central tendency because it is based on all observations in the dataset. While it can be influenced by extreme outliers, it remains mathematically consistent and is less subject to sampling fluctuations compared to other measures like the range or mode in many distributions.
1064
Which of the following measures is classified as an order statistic?
Order statistics are values in a sample listed in ascending or descending order. The median is the middle value of an ordered dataset, making it a fundamental order statistic. Other measures like the arithmetic mean (A.M) depend on the sum of all values rather than their relative order.
1065
How are measures such as the median, mode, deciles, and percentiles collectively classified in statistics?
These measures are known as averages of position (or partition values) because they depend on the relative position of values in an ordered dataset, rather than being calculated through algebraic operations on all data points like the arithmetic mean.
1066
Which statistical measure requires the dataset to be ordered before calculation?
The median is a positional average. To find the middle value, the dataset must be sorted in ascending or descending order. Other measures like the mean or mode do not strictly require the data to be sorted to perform the calculation, although sorting can assist in finding the mode.
1067
Which measure of central tendency is calculated by dividing the sum of all data values by the total number of observations?
The arithmetic mean is the most common measure of central tendency. It is computed by summing all individual values in a dataset and dividing that sum by the total count of observations. It provides a representative value for the center of the data, assuming the data is interval or ratio scaled.
1068
Which category of measures is used to summarize data using central tendency, variation, and distribution shape?
Descriptive statistics are used to summarize and describe the main features of a dataset. These include measures of central tendency (like mean, median, mode), measures of dispersion (like range, variance, standard deviation), and measures of shape (like skewness and kurtosis), which collectively provide a comprehensive summary of the data distribution.
1069
What is the mathematical property of the sum of absolute deviations taken from the median?
A fundamental property of the median is that the sum of the absolute differences between each data point and the median is smaller than the sum of the absolute differences between the data points and any other value. This makes the median a robust measure of central tendency compared to the mean, which minimizes the sum of squared deviations.
1070
Calculate the arithmetic mean of the values 10, 8, 6, 4, and 2.
The arithmetic mean is calculated by summing all values and dividing by the total count. The sum is 10 + 8 + 6 + 4 + 2 = 30. There are 5 values. The mean is 30 / 5 = 6. Note: The provided answer key 'B' (15) appears factually incorrect based on standard arithmetic. 30/5 equals 6.
