NRES 2 Prelim

• Population: The entire group of individuals or instances about whom we want to draw conclusions.
• Sample: A subset of the population that is selected for study. It's often impractical or impossible to study an entire population, so researchers select a sample to make inferences about the population
• Variable: A characteristic or attribute that can take different values. For example, height, weight, age, and test scores are variables.
• Data: The values or observations of a variable that are collected from a sample or population.
• Descriptive Statistics: Methods used to summarize and describe the main features of a data set. Examples include measures of central tendency (mean, median, mode) and measures of dispersion (range, variance, standard deviation).
• Inferential Statistics: Techniques used to make predictions or inferences about a population based on a sample of data.
• Mean: The average of a set of values. It is calculated by summing all the values and dividing by the number of observations.
• Median: The middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of observations, the median is the average of the two middle values.
• Mode: The value that appears most frequently in a data set.
• Range: The difference between the maximum and minimum values in a data set
• Standard Deviation: A measure of the amount of variation or dispersion in a set of values. It provides an indication of how spread out the values are around the mean.
• Normal Distribution: A symmetric, bell-shaped probability distribution.
• In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.
• Hypothesis Testing: A statistical method used to make inferences about a population based on a sample of data. It involves formulating a hypothesis, collecting and analyzing data, and drawing conclusions.
• Confidence Interval: A range of values used to estimate the true value of a population parameter. It provides a level of confidence that the true value falls within the interval
• Regression: A statistical method used to examine the relationship between two or more variables. It helps in predicting one variable based on the values of others
• Histograms - A graphical representation of the distribution of numerical data.
• Scatter Plots - Displays the relationship between two variables.
• Line Charts - Connects data points with straight lines.
• Histograms - It consists of bars representing the frequency of data within intervals or bins.
• Scatter Plots - Each point on the plot represents a pair of values for the two variables
• Line Charts - Useful for showing trends over time or relationships between two variables.
• Bar Charts - Represents categorical data with rectangular bars.
• bar charts - The length of each bar corresponds to the quantity it represents.
• Pie Charts - Divides a circle into sectors to represent data proportions.
• Pie Charts - Useful for showing the composition of a whole.
• Descriptive data analysis is the process of summarizing, organizing, and presenting data in a meaningful and informative way.
• Descriptive data analysis - Objective: It aims to describe the main features of a dataset, providing a clear and concise summary that facilitates understanding.
• Descriptive data analysis Methods - Measures of Central Tendency, Measures of Dispersion, Frequency Distribution, Percentiles, Skewness and Kurtosis:
• Mean - The arithmetic average of a set of values
• Mean - Properties: Influenced by extreme values (outliers), and it may not be a representative value if the distribution is skewed.
• Median - The middle value in a dataset when it is ordered. If there is an even number of observations, the median is the average of the two middle values
• Median - Calculation: Arrange data in ascending order and find the middle value.
• Mean - Properties - Less sensitive to outliers than the mean; suitable for skewed distributions
• Mode - Definition - The value that occurs most frequently in a dataset.
• Mode - Properties: A dataset can have no mode, one mode (unimodal), or multiple modes (multimodal).
• Mode - Particularly useful for categorical data.
• Range - the difference between the maximum and minimum values
• Variance - the average of the squared differences from the mean
• Standard Deviation - the square root of the variance, representing the average deviation from the mean