Chapter 2 Flashcards
Define absolute frequency in the context of frequency distributions.
Absolute frequency (f) refers to the number of times a certain value occurs in a distribution.
How are nominal values listed in frequency distributions?
Nominal values are listed in any order in frequency distributions.
Explain the significance of relative frequency in data analysis.
Relative frequency (rf) allows for comparison of how often a value occurs relative to the total number of values, making it useful for comparing groups of different sizes.
Describe the types of variables and their order in frequency distributions.
Ordinal, interval, and ratio variables are listed from highest to lowest, while nominal values can be listed in any order.
Describe absolute frequency in the context of data analysis.
Absolute frequency refers to the number of times each given value is observed within a dataset, such as the number of homosexual and heterosexual couples in a study.
Define the significance of comparing absolute and relative frequency.
Comparing absolute and relative frequency is significant for understanding data from groups of different sizes or when a single group has an unusual size, making the data easier to interpret.
How can percentages be derived from relative frequency?
Percentages can be derived from relative frequency by multiplying the relative frequency by 100.
Explain the importance of using relative frequency in data analysis.
Using relative frequency is important because it allows for meaningful comparisons between groups of different sizes, providing a clearer understanding of the data.
Describe the process of calculating Cumulative Relative Frequency.
Cumulative Relative Frequency is calculated by dividing each cumulative frequency by the total number of observations.
How does Cumulative Relative Frequency enhance data interpretation?
Cumulative Relative Frequency provides more meaningful conclusions than cumulative frequency alone.
What is the significance of using equal sized intervals when grouping data?
Equal sized intervals ensure consistency in data representation and facilitate easier comparison and analysis.
Explain the concept of mutually exclusive intervals in data grouping.
Mutually exclusive intervals mean that each data point can only belong to one interval, preventing overlap and ensuring clarity in categorization.
Describe a grouped frequency distribution.
A grouped frequency distribution organizes data into intervals, showing the frequency of data points within each interval.
Define the purpose of sentencing time in a grouped frequency distribution.
Sentencing time in a grouped frequency distribution is used to analyze the duration of sentences given to youth for identical crimes and similar histories.
How are intervals determined in a grouped frequency distribution?
Intervals in a grouped frequency distribution are determined by setting an interval width and calculating the midpoint of each interval.
What is meant by equal width in a grouped frequency distribution?
Equal width in a grouped frequency distribution means that each interval has the same range of values.
Explain the concept of mutually exclusive intervals.
Mutually exclusive intervals in a grouped frequency distribution ensure that each data point falls into one and only one interval, preventing overlap.
How can the midpoint of an interval be calculated?
The midpoint of an interval can be calculated by averaging the lower and upper boundaries of the interval.
Describe the concept of exact limits of intervals in relation to continuous variables.
Exact limits of intervals refer to the boundaries that define the range of values for continuous variables, determined by the precision of the data.
How are exact intervals determined based on the precision of data?
Exact intervals are determined by adding and subtracting half of the smallest unit of measurement from the measured value.
Define the exact limits for a measurement of ‘2’ when rounded to the nearest whole number.
The exact limits for a measurement of ‘2’ rounded to the nearest whole number are 1.5 and 2.5.
Explain the significance of levels of precision in measurements.
Levels of precision indicate how finely a measurement is made, affecting the exact limits of the interval around that measurement.
How should axes be handled in graphing distributions?
Axes that do not begin at zero should be broken.
Explain the use of bar graphs in data representation.
Bar graphs are used for discrete data on the x-axis, where each bar represents a possible value of a variable.
What does the height of a bar in a bar graph represent?
The height of the bar indicates the frequency with which the value occurred.
Identify the types of data that can be depicted on the y-axis of a bar graph.
The y-axis can depict ordinal, interval, and ratio data.
Differentiate between single and multiple bar graphs.
Single bar graphs display one set of data, while multiple bar graphs can show comparisons between different sets of data.
Describe the characteristics of a histogram.
A histogram displays continuous data on the x-axis with attached bars, where intervals have exact limits defined as plus or minus half of the smallest unit of measurement.
How are the limits of intervals in a histogram defined?
The limits of intervals in a histogram are defined as exact limits, which are plus or minus half of the smallest unit of measurement.
Explain the difference between a histogram and a frequency polygon.
A histogram uses bars to represent data, while a frequency polygon uses points plotted over the midpoints of intervals.
Define the term ‘midpoint’ in the context of a frequency polygon.
The midpoint in a frequency polygon is the value that lies in the center of an interval, such as 17 for the interval 15-19.
How are points represented in a frequency polygon?
Points in a frequency polygon are plotted over the midpoints of intervals, connecting them to form a line.
What is the significance of apparent limits in a histogram?
Apparent limits may provide clearer or more meaningful labels on the graph, but the exact limits are crucial for data analysis.
Describe the type of graph suitable for comparing socioeconomic status between Floridians and Californians.
A comparative bar graph or a box plot would be suitable for visualizing the differences in socioeconomic status between the two groups.
Define an ogive in the context of statistical data representation.
An ogive is a cumulative frequency graph that shows the number of observations below a particular value, allowing for the determination of relative standing.
How can you determine the relative standing of a value in a dataset?
Relative standing can be determined by calculating the cumulative frequency and identifying the percentile rank of the value within the dataset.
Do cumulative frequency polygons help in understanding data distribution?
Yes, cumulative frequency polygons provide a visual representation of the cumulative frequencies, helping to understand the distribution and trends in the data.
Explain how to find the value needed to be in the 10th percentile of a dataset.
To find the value needed to be in the 10th percentile, calculate the cumulative frequency and identify the data point that corresponds to 10% of the total observations.
What is the significance of plotting cumulative frequency over the upper exact limit of each interval?
Plotting cumulative frequency over the upper exact limit of each interval allows for a clear representation of how many data points fall below each threshold, aiding in the analysis of data distribution.
Describe the characteristics of frequency distributions.
Frequency distributions can be characterized by symmetry (symmetrical vs. skewed) and kurtosis (spread or scatter of observed values).
Define skewness in the context of frequency distributions.
Skewness refers to the asymmetry of a distribution, where the majority of observations are concentrated on one side.
How can you identify a positively skewed distribution?
A positively skewed distribution has a tail that points toward the right, indicating that the majority of observations are concentrated on the left.
How can you identify a negatively skewed distribution?
A negatively skewed distribution has a tail that points toward the left, indicating that the majority of observations are concentrated on the right.
Explain the concept of kurtosis in frequency distributions.
Kurtosis refers to the spread or scatter of observed values in a distribution, indicating how peaked or flat the distribution is.
Define kurtosis in the context of data distribution.
Kurtosis is an indication of variability within data relative to a normal distribution.
Describe the characteristics of a platykurtic distribution.
A platykurtic distribution is flat compared to a normal distribution.
What is a leptokurtic distribution?
A leptokurtic distribution is skinny compared to a normal distribution.
How does a mesokurtic distribution compare to a normal distribution?
A mesokurtic distribution is moderate and resembles a normal distribution.
