Statistics Flashcards

A unique kind of index number is —————.

Answer: Average

An index number measures the change in a variable or group of variables over time, relative to a base period. While not an index number itself, an average can serve as a unique kind of reference point or a summary statistic from which an index number might be constructed or compared, representing a typical value in a dataset.

The measurements required to determine the variation between the observations in the variable's unit are known as:

Answer: Absolute measures of dispersion

Absolute measures of dispersion quantify the spread or variability within a dataset using the original units of the data. These measures, such as range, variance, and standard deviation, directly indicate the extent of variation in the same units as the observations.

The numbers are 78, 56, 22, 34, 45, 54, 39, 68, 54, and 84. What is the median?

Answer: 54

To find the median, first arrange the numbers in ascending order: 22, 34, 39, 45, 54, 54, 56, 68, 78, 84. Since there are 10 numbers (an even count), the median is the average of the two middle numbers. The 5th and 6th numbers are 54 and 54, so their average is (54 + 54) / 2 = 54.

Which of the following best describes the dispersion in an absolute sense?

Answer: Standard deviation

Standard deviation is a widely used absolute measure of dispersion that quantifies the average amount of variation or spread of data points around the mean. It is expressed in the same units as the original data, providing a direct and interpretable measure of variability.

Which of the following is not utilized to summarize data in a five-number summary?

Answer: the 25th percentile

A five-number summary consists of the minimum value, the first quartile (Q1 or 25th percentile), the median (Q2), the third quartile (Q3), and the maximum value. Therefore, the 25th percentile is a core component of the five-number summary, representing the point below which 25% of the data falls.

The only two observations required for the dispersion measure are:

Answer: Range

The range is the simplest measure of dispersion, calculated by subtracting the minimum value from the maximum value in a dataset. It only requires these two extreme observations to determine the overall spread of the data.

A measure of is a single value that attempts to describe a set of data by identifying the central position within that set of

Answer: Central Tendency

Measures of central tendency are statistical values that aim to describe a set of data by identifying the central or typical position within that set. Common examples include the mean, median, and mode, which each represent the 'center' in a different way.

A sequence of values scattered around the average are referred to as:

Answer: Dispersion

Dispersion, also known as variability or spread, refers to how stretched or squeezed a distribution of data is. It quantifies the extent to which individual data points differ from each other and from the central tendency (average), indicating the spread of values.

When the median is 13 and the mean is 11, the mode value is

Answer: 17

For moderately skewed distributions, there is an empirical relationship between the mean, median, and mode: Mode ≈ 3 * Median - 2 * Mean. Given a median of 13 and a mean of 11, the mode can be estimated as 3 * 13 - 2 * 11 = 39 - 22 = 17.

For qualitative data, the ideal average is

Answer: median

For qualitative data, especially ordinal data where categories have a natural order, the median is an ideal measure of central tendency. It identifies the middle category or value when the data is arranged in order, providing a central point without requiring numerical calculations like the mean.

What average's sum of deviations equals zero?

Answer: Mean

The mean (arithmetic average) possesses a unique property where the sum of the deviations of each data point from the mean is always zero. This characteristic makes the mean the balancing point of a dataset, representing its central equilibrium.