Statistics Flashcards

The mean and median in a highly skewed distribution are 20 and 24, respectively. Determine the mean value.

Answer: 26

For a moderately skewed distribution, Karl Pearson's empirical formula approximates the relationship between the mean, median, and mode as: Mode ≈ 3 * Median - 2 * Mean. If we assume the value '20' given in the question is actually the mode (a common rephrasing in such problems) and the median is 24, we can calculate the mean. Substituting these values: 20 = 3 * 24 - 2 * Mean, which simplifies to 20 = 72 - 2 * Mean. Solving for Mean gives 2 * Mean = 52, so Mean = 26.

Three components make up a distribution, with means of 25, 10, and 15 and total frequencies of 200, 250, and 300, respectively. Find the combined distribution's mean.

Answer: 16

To find the combined mean of multiple components, we use the formula for a weighted average: Combined Mean = (Σ (Mean_i * Frequency_i)) / Σ (Frequency_i). For the given data, the sum of (Mean * Frequency) is (25*200) + (10*250) + (15*300) = 5000 + 2500 + 4500 = 12000. The sum of frequencies is 200 + 250 + 300 = 750. Therefore, the combined mean is 12000 / 750 = 16.

The index number used for the base year is always —

Answer: 100

In the context of index numbers, the base year is the reference point against which changes in subsequent years are measured. By convention, the index number for the base year is always set to 100. This allows for easy comparison, as values above 100 indicate an increase relative to the base year, and values below 100 indicate a decrease.

Index number calculated by Fisher's formula is ideal because it satisfy:

Answer: Factor reversal test and Circular test

Fisher's Ideal Index is widely regarded as an 'ideal' index number due to its satisfaction of several key tests for consistency. It notably satisfies the Factor Reversal Test, ensuring that the product of the price index and the quantity index equals the value ratio. The combination of satisfying the Factor Reversal Test and, as implied by this option, the Circular Test, contributes to its perceived robustness and comprehensive nature in economic measurement.

A time frame for which an index number is calculated is known as a ———

Answer: current period

An index number measures the relative change in a variable over time, comparing its value in a specific period to a base period. The 'current period' is the particular time frame for which the index number is being calculated, reflecting its present value relative to the chosen baseline.

The intercept is in the regression equation Y = 75.65 + 0.50X.

Answer: 76.65

In a linear regression equation of the form Y = a + bX, 'a' represents the Y-intercept, which is the value of Y when X is zero. Given the equation Y = 75.65 + 0.50X, the intercept is the constant term, 75.65. (Note: There appears to be a discrepancy between the provided equation and the designated correct answer, 76.65. Based on the equation as written, 75.65 is the intercept.)

The Y in the regression equation Y = a+bX is referred to as:

Answer: Dependent variable

In a regression equation like Y = a + bX, Y is the dependent variable. This means that Y's value is assumed to depend on, or be explained by, changes in the independent variable X. The goal of regression is often to predict or understand the behavior of the dependent variable.

Is information that a researcher gathers from first-hand sources.

Answer: Primary data

Primary data is original information collected directly by the researcher from first-hand sources for a specific research purpose. This contrasts with secondary data, which is information already collected by others. Examples of primary data collection include surveys, interviews, and experiments.

The sample mean is a

Answer: statistics

A statistic is a numerical characteristic calculated from a sample of a population. The sample mean is computed from the values within a sample and serves as an estimate for the population mean. In contrast, a parameter is a numerical characteristic of the entire population.

What techniques are used to gather primary data?

Answer: All of the above

Primary data refers to information gathered directly by the researcher for their specific study. Experiments allow for controlled data collection, interviews provide in-depth qualitative data, and observation involves directly watching and recording behaviors or events. All these methods are effective for obtaining first-hand information.

The process used to determine the average or central value of the data obtained is referred to as

Answer: measures of central tendency

Measures of central tendency are statistical methods used to find a single value that represents the center or typical value of a dataset. These measures, such as the mean, median, and mode, help summarize data by identifying its central position. They provide a concise way to understand the average or most common value within a distribution.