Statistical Data Types and Frequency

A rule for determining the number of classes needed in a frequency distribution. It is calculated as: # = 1.3.3 log10 n, where n is the number of observations.

To summarize information from frequency distributions and graphs by finding a single value that represents the center or typical value of the data.

They describe how spread out or varied the data is. This helps us understand the distribution of the data and whether there is a lot of variability or not.

The arithmetic mean is the sum of all values divided by the number of values. The geometric mean is calculated as the n-th root of the product of n values. While the arithmetic mean is the average of the numbers, the geometric mean is the average of the factors.

It measures the spread of the data points around the mean. It is calculated as the square root of the variance.

Formula: √∑(X - X̄)² / n

It's a way to summarize a set of numbers by providing a single value that represents the 'center' or 'average' of the dataset. It is calculated by adding all the numbers in the set and dividing by the total number of values.

The foundation of probability theory is based on the idea of an event or outcome that can occur in an experiment. The occurrence of an event is uncertain and may be influenced by chance.

It represents the sum of all values in a set. It commonly appears in formulas for various statistical calculations, such as mean, variance, and standard deviation.

It represents the relative variability of the mean. It is calculated by dividing Standard Deviation by Mean. A higher coefficient of variation indicates greater variability, whereas a lower coefficient of variation indicates less variability.

It represents the number of standard deviations a data point is away from the mean. A positive Z-score means the data point is above the mean, while a negative z-score means it’s below the mean.

It refers to the frequency of an event or outcome in relation to the total number of possible events. It reflects the observed probability of an event based on empirical data.

It represents the mean of the population. It is used to estimate the average value of a variable across an entire population.

Laplace's Rule of Succession is a method for estimating the probability of an event based on a limited number of observations. It assumes that all possible events are equally likely.

The principle states that the probability of at least one of several mutually exclusive events occurring is equal to the sum of their individual probabilities. Formula: P(A or B) = P(A) + P(B)

The probability of two events A and B occurring one after the other is called composite probability.

Two events are said to be dependent if the occurrence of one event influences the probability of the other event occurring.

Example: The probability of drawing a red card from a deck of cards is dependent on whether a red card has already been drawn.

This probability considers the combined effect of multiple events occurring in a specific order. It calculates the probability of event B occurring given that event A has already occurred.

The probability of one event occurring given that another event has already occurred. Formula: P(A|B) = P(A and B) / P(B)

An experiment that produces random outcomes. The results are uncertain and can vary even with repeated trials.

It is the set of all possible outcomes of a random experiment. It encompasses every possible result that can occur.

These errors are systematic and occur consistently in a particular direction. These errors arise from flaws in the measurement instrument or design of the experiment.

These errors are random and occur without any pattern or bias. They are caused by chance occurrences and fluctuations in the measurement process.

An accurate measurement is characterized by its proximity to the true value. If the measurement is close to the actual value, it is considered accurate.

Ordinal data can be logically ordered or ranked, while nominal data cannot. Data like 'strongly agree', 'agree', 'disagree' are ordinal. Data like 'male', 'female' are nominal.

Data intensity refers to the 'strength' or value of the measured phenomenon. It represents the actual quantity or magnitude of the variable being studied.

Raw data is in its original, unorganized form. It is the primary data collected during an experiment or observation and often includes unprocessed information.

The object of investigation refers to the phenomenon or event that is being observed and studied in a statistical investigation. It is the subject of interest for analysis.

In statistics, a 'variable' is a characteristic that can vary or change within a population. It can be quantitative (expressed as numbers) or qualitative (expressed as categories).