Quick reminder is this a central tendency - spread - symmetry question(2)
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This document discusses three types of questions about data distribution: central tendency, which represents the average or most common data point; spread, which is the dispersion or range of scores around the central tendency; and symmetry, which is the shape of the distribution and whether it is symmetrical or asymmetrical. Keywords for each type are provided.
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Basic statisctis -Anandh Shankar
Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.
Measures of central tendency
Measures of central tendency are values that are central to a data set or distribution. The three most common measures are the mean, which is the average value calculated by dividing the sum of all data points by the total number of data points; the median, which is the middle value of the data set with half of the values above it and half below it; and the mode, which is the data value that occurs most frequently.
Central Tendency and types
Central tendency refers to measures that describe the center of a dataset and includes the mean, median, and mode. The mean is calculated by adding all values and dividing by the total number of values. The median is the middle number in a dataset listed in ascending order. The mode is the most frequently occurring number in the dataset.
Measures of central tendency
The document discusses different measures of central tendency:
- The mode is the most frequent score in a data set and is used for nominal data.
- The median is the middle score when data is arranged from lowest to highest and is not influenced by outliers.
- The mean is the average of all scores, calculated by summing all scores and dividing by the total number, and is preferred for interval/ratio scaled and non-skewed data.
Skewness of random variable
Skewness measures the symmetry of a probability distribution and is calculated by subtracting the median from the mean, multiplying by 3, and dividing by the standard deviation. A skewness between -1 and 1 is highly skewed, between -1 and -0.5 or 0.5 to 1 is moderately skewed, and between -0.5 to 0.5 is approximately symmetrical. If the mean equals the median, the distribution is symmetrical. If the mean is less than the median it is negatively skewed, and if the mean is greater it is positively skewed.
Normal distrubutions
The normal distribution is the most important and widely used distribution in statistics. It is bell-shaped and symmetric around the mean. The normal distribution is defined by its mean and standard deviation. It has several key properties: it is symmetric, asymptotic, with the mean, median and mode all in the middle. The standard normal distribution is a special case where the mean is 0 and standard deviation is 1. It follows the empirical rule where about 68%, 95%, and 99% of observations fall within 1, 2, and 3 standard deviations of the mean.
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The document discusses measures of central tendency including the mean, median, and mode for ungrouped data sets.
The mean is the average and is calculated by adding all values in the data set and dividing by the number of values. The median is the middle number when data is arranged in order. For even data sets, the median is the average of the two middle numbers. The mode is the number that occurs most frequently in the data set. Sometimes there are multiple modes or no mode. The range is the difference between the highest and lowest values in the data set.
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Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.
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Measures of central tendency are values that are central to a data set or distribution. The three most common measures are the mean, which is the average value calculated by dividing the sum of all data points by the total number of data points; the median, which is the middle value of the data set with half of the values above it and half below it; and the mode, which is the data value that occurs most frequently.
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Skewness measures the symmetry of a probability distribution and is calculated by subtracting the median from the mean, multiplying by 3, and dividing by the standard deviation. A skewness between -1 and 1 is highly skewed, between -1 and -0.5 or 0.5 to 1 is moderately skewed, and between -0.5 to 0.5 is approximately symmetrical. If the mean equals the median, the distribution is symmetrical. If the mean is less than the median it is negatively skewed, and if the mean is greater it is positively skewed.
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The normal distribution is the most important and widely used distribution in statistics. It is bell-shaped and symmetric around the mean. The normal distribution is defined by its mean and standard deviation. It has several key properties: it is symmetric, asymptotic, with the mean, median and mode all in the middle. The standard normal distribution is a special case where the mean is 0 and standard deviation is 1. It follows the empirical rule where about 68%, 95%, and 99% of observations fall within 1, 2, and 3 standard deviations of the mean.
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The standard deviation, like the mean, is used to analyze scaled, normally distributed data such as speed, weight, height, and temperature. It measures how spread out numbers are from the average (mean) value. The mean should only be used when the data follows a more or less normal distribution, as outliers in skewed distributions overly influence the mean.
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Quick reminder is this a central tendency - spread - symmetry question
Central Tendency, Spread, and Distribution Shape are three types of questions related to how data is organized in a distribution. Central Tendency represents the middle point where data scores cluster, Spread refers to the dispersion of scores around the central point, and Distribution Shape describes whether the data is normally distributed, skewed, or another pattern.
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relationship between dispersion and central tendency
Solution
Central tendency refers to and locates the center of the distribution of values. Mean, mode, and
median are the most commonly used indices in describing the central tendency of a data set. If a
data set is symmetric, then both the median and the mean of the data set coincide with each
other.
Dispersion is the amount of spread of data about the center of the distribution. Range and
standard deviation are the most commonly used measures of dispersion.
Two kinds of statistics are frequently used to describe data. They are measures of central
tendency and dispersion. These are often called descriptive statistics because they can help you
describe your data.
THE RELATIONSHIP BETWEEN DISPERSION AND CENTRAL TENDENCY IS THAT
ARE DESCRIPTIVE STATISTICS THAT CAN HELP YOU TO DESCRIBE THE DATA
THAT YOU ARE INVESTIGATING.
SUMMARY MEASURES.pdf
This document discusses various measures of central tendency and dispersion that are commonly used in epidemiology to summarize data distributions. It describes the mean, median and mode as measures of central tendency that convey the average or typical value, and how the appropriate measure depends on the data's measurement level, shape and research purpose. Measures of dispersion like range, interquartile range, variance and standard deviation describe how spread out the data is from the central value. The document provides formulas and explanations for calculating and interpreting each measure.
Biostatistics basics-biostatistics4734
This document provides an introduction to common statistical terms and concepts used in biostatistics. It defines key terms like variables, populations, samples, descriptive statistics, and levels of measurement. It also explains how to calculate measures of central tendency like mean, median, and mode. Additionally, it describes properties of normal and skewed distributions, how to interpret standard deviation as a measure of variability, and how to calculate standard deviation in Excel.
Biostatistics basics-biostatistics4734
This document provides an introduction to common statistical terms and concepts used in biostatistics. It defines key terms like variables, populations, samples, descriptive statistics, and levels of measurement. It also explains how to calculate measures of central tendency like mean, median, and mode. Additionally, it describes properties of normal and skewed distributions, how to interpret the shape of data, and how to calculate and interpret standard deviation as a measure of variability.
Introduction to Descriptive Statistics
Lecture on Introduction to Descriptive Statistics - Part 1 and Part 2. These slides were presented during a lecture at the Colombo Institute of Research and Psychology.
Central spread - symmetry (jejit + indepth)
The document discusses different categories of methods for analyzing data distributions: central tendency, spread, and symmetry. Central tendency describes where data are clustered around the average or center. Spread describes how far data are from the middle. Symmetry describes the overall shape of the distribution. The document provides examples of questions that would require analyzing the central tendency, spread, or symmetry and instructs the reader to identify which one is most relevant. It emphasizes that every distribution has all three characteristics but the analysis may focus on one aspect.
Central spread - symmetry (jejit + indepth)
The document discusses different categories of methods for analyzing data distributions: central tendency, spread, and symmetry. Central tendency describes where data are clustered around the average or center. Spread describes how far data are from the middle. Symmetry describes the overall shape of the distribution. The document provides examples of questions that would require analyzing the central tendency, spread, or symmetry and instructs the reader to identify which one is most relevant. It emphasizes that every distribution has all three characteristics but the analysis may focus on one aspect.
Measures of central tendency and dispersion
This document provides an overview of measures of central tendency and dispersion that are commonly used in descriptive statistics. It defines and provides examples of the mean, median, mode, range, and standard deviation. It also discusses frequency tables, histograms, and the shapes that distributions can take. The goal of descriptive statistics is to summarize and describe data through techniques like these in order to understand the characteristics of variables.
Statistics
this presentation is all about central tendency, skewness, kurtosis, Wilcox rank test. these all terms are used in statistics.
BRM_Data Analysis, Interpretation and Reporting Part II.ppt
This document provides an overview of data analysis, interpretation, and reporting. It discusses descriptive and inferential analysis, and univariate, bivariate, and multivariate analysis. Specific quantitative analysis techniques covered include measures of central tendency, dispersion, frequency distributions, histograms, and tests of normality. Hypothesis testing procedures like t-tests, ANOVA, and non-parametric alternatives are also summarized. Steps in hypothesis testing include stating the null hypothesis, choosing a statistical test, specifying the significance level, and deciding whether to reject or fail to reject the null hypothesis based on findings.
ANALYSIS ANDINTERPRETATION OF DATA Analysis and Interpr.docx
ANALYSIS AND
INTERPRETATION
OF DATA
Analysis and Interpretation of Data
https://my.visme.co/render/1454658672/www.erau.edu
Slide 1 Transcript
In a qualitative design, the information gathered and studied often is nominal or narrative in form. Finding trends, patterns, and relationships is discovered inductively and upon
reflection. Some describe this as an intuitive process. In Module 4, qualitative research designs were explained along with the process of how information gained shape the inquiry as it
progresses. For the most part, qualitative designs do not use numerical data, unless a mixed approach is adopted. So, in this module the focus is on how numerical data collected in either
a qualitative mixed design or a quantitative research design are evaluated. In quantitative studies, typically there is a hypothesis or particular research question. Measures used to assess
the value of the hypothesis involve numerical data, usually organized in sets and analyzed using various statistical approaches. Which statistical applications are appropriate for the data of
interest will be the focus for this module.
Data and Statistics
Match the data with an
appropriate statistic
Approaches based on data
characteristics
Collected for single or multiple
groups
Involve continuous or discrete
variables
Data are nominal, ordinal,
interval, or ratio
Normal or non-normal distribution
Statistics serve two
functions
Descriptive: Describe what
data look like
Inferential: Use samples
to estimate population
characteristics
Slide 3 Transcript
There are, of course, far too many statistical concepts to consider than time allows for us here. So, we will limit ourselves to just a few basic ones and a brief overview of the more
common applications in use. It is vitally important to select the proper statistical tool for analysis, otherwise, interpretation of the data is incomplete or inaccurate. Since different
statistics are suitable for different kinds of data, we can begin sorting out which approach to use by considering four characteristics:
1. Have data been collected for a single group or multiple groups
2. Do the data involve continuous or discrete variables
3. Are the data nominal, ordinal, interval, or ratio, and
4. Do the data represent a normal or non-normal distribution.
We will address each of these approaches in the slides that follow. Statistics can serve two main functions – one is to describe what the data look like, which is called descriptive statistics.
The other is known as inferential statistics which typically uses a small sample to estimate characteristics of the larger population. Let’s begin with descriptive statistics and the measures
of central tendency.
Descriptive Statistics and Central Measures
Descriptive statistics
organize and present data
Mode
The number occurring most
frequently; nominal data
Quickest or rough estimate
Most typical value
Measures of central
tendenc.
Measures of central tendency
The document discusses different measures of central tendency including the mean, median, and mode. The mean is the average value and considers all scores, but can be impacted by outliers. The median is the middle value when scores are arranged in order and is less impacted by outliers. The mode is the most frequently occurring value and can be used for both numerical and categorical data, but may not always indicate the true central tendency. Each measure has advantages and limitations, and different measures are better suited for certain types of data distributions.
Central tendency
This document discusses measures of central tendency. It defines central tendency as a statistical measure that identifies a single value that best represents an entire data set. The three main measures are the mean, median, and mode.
The mean is the average value, calculated by summing all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the most frequently occurring value.
The document provides examples and formulas to calculate each measure. It also discusses advantages and disadvantages of each, and gives examples of how they are used in daily life situations like measuring student test scores or transportation usage.
Frequency distributions.pptx
This document discusses key concepts related to frequency distributions and analyzing distributions of data, including:
- Frequency distributions group data into classes and show the number of observations in each class. Bar charts and pie charts can represent this.
- Properties of distributions like shape (symmetric vs. skewed), central tendency (mean, median, mode), and variability/spread (range, standard deviation) provide important information.
- Normal distributions form a symmetrical, bell-shaped curve where most scores fall within one standard deviation of the mean. Standard deviation measures average distance from the mean.
Descriptive Statistics: Measures of Central Tendency - Measures of Dispersion...
Descriptive Statistics - Measures of Central Tendency (Mean - Median - Mode) - Measures of Dispersion ( Normal Curve - Co-efficient of Variation )
initial postWhat are the characteristics, uses, advantages, and di.docx
initial post
What are the characteristics, uses, advantages, and disadvantages of each of the measures of location and measures of dispersion? Discuss them with examples
first reply
Measures of location and measures of dispersion are two different ways of describing quantitative variables. Measures of location are often known as averages. Measures of dispersion are often known as a variation or spread. Both measures are helpful with describing statistical information. (Lind, Marchal, & Wathen, 2015)
The different measures of location include: the arithmetic mean, the median, the mode, the weighted mean, and the geometric mean. All of these measures of location pinpoint the center of a distribution of data. An advantage of measures of location is that the averages show us the central value of the data. A disadvantage of only using measures of location is that we may not draw an accurate conclusion because an average does not tell the spread of the data. Some examples of using measures of location include: finding the average price of a concert ticket, finding the average age of homeowners in a community, finding the averages shoe size of boys between the ages of 13-19, and finding the average amount of money people spend on food annually. (Lind, Marchal, & Wathen, 2015)
The different measures of dispersion include: the range, the variance, and the standard deviation. All of these measures of dispersion tell us about the spread of the data and it helps us compare the spread in two or more distributions. Advantages of using measures of dispersion are that it gives us a better idea of the range in which an average was calculated, and it is easy to calculate and understand. A disadvantage of using measures of dispersion is that it is a broad measurement because it only shows the maximum and minimum values of data. For example, the salaries of dentists in the state of Georgia might range from $70,000-$120,000 (just a made up example – not necessarily accurate data). This information is great for someone to know the range of dentist salaries, but it lacks in showing specific information about dentists’ salaries. (Lind, Marchal, & Wathen, 2015)
Lind, D. A., Marchal, W. G., & Wathen, S. A. (2015). Statistical techniques in business & economics. New York, NY: McGraw-Hill Education.
Second Reply
What are the characteristics, uses, advantages, and disadvantages of each of the measures of location and measures of dispersion? Discuss them with examples.
These are the measures in common use of location and dispersion: arithmetic mean, median, mode, weighted mean, and geometric mean. The arithmetic mean, median, and mode The mean usually refers to the arithmetic mean or average. This is just the sum of the measurements divided by the number of measurements. We make a notational distinction between the mean of a population and the mean of a sample. The general rule is that Greek letters are used for population characteristics and Latin letters ar.
Central tendency spread - symmetry (4.0)
The document discusses different types of descriptions for distributions including central tendency, spread, and symmetry. It provides examples of questions that would require analyzing the central tendency, spread, or symmetry of a distribution to answer. The document is intended to help the reader identify which type of distribution description is most relevant for answering different types of questions.
Standard Deviation, Standard Error
Standard deviation (SD) and standard
error (SE) are quietly but extensively used
in biomedical publications. These terms
and notations are used as descriptive statistics (summarizing numerical data), and
they are used as inferential statistics (estimating population parameters from samples). I review the use and misuse of SD
and SE in several authoritative medical
journals and make suggestions to help
clarify the usage and meaning of SD and
SE in biomedical reports
These is info only ill be attaching the questions work CJ 301 – .docx
This document discusses measures of variability and dispersion in descriptive statistics. It defines variability as how scores differ from each other or from the mean. Four measures of dispersion are discussed: range, mean deviation, variance, and standard deviation. Standard deviation is described as the average distance from the mean and the most commonly used measure. Examples are provided to demonstrate how to calculate standard deviation step-by-step. The standard deviation is then used to estimate what percentage of values fall within certain ranges from the mean based on the normal distribution curve.
Similar to Quick reminder is this a central tendency - spread - symmetry question(2) (20)
Quick reminder is this a central tendency - spread - symmetry question
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relationship between dispersion and central tendencySolutionCe.pdf
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BRM_Data Analysis, Interpretation and Reporting Part II.ppt
BRM_Data Analysis, Interpretation and Reporting Part II.ppt
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Descriptive Statistics: Measures of Central Tendency - Measures of Dispersion...
Descriptive Statistics: Measures of Central Tendency - Measures of Dispersion...
initial postWhat are the characteristics, uses, advantages, and di.docx
initial postWhat are the characteristics, uses, advantages, and di.docx
These is info only ill be attaching the questions work CJ 301 – .docx
These is info only ill be attaching the questions work CJ 301 – .docx
More from Ken Plummer
Diff rel gof-fit - jejit - practice (5)
The document discusses the differences between questions of difference, relationship, and goodness of fit. It provides examples to illustrate each type of question. A question of difference compares two or more groups on some outcome, like comparing younger and older drivers' average driving speeds. A question of relationship examines whether a change in one variable causes a change in another, such as the relationship between age and flexibility. A question of goodness of fit assesses how well a claim matches reality, such as whether a salesman's claim of software effectiveness fits the results of user testing.
Learn About Range - Copyright updated
This document provides examples of questions that ask for the lowest and highest number in a set of data. The questions ask for the difference between the state with the lowest and highest church attendance, the students with the highest and lowest test scores, and the slowest and fastest versions of a vehicle model.
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The document discusses the differences between descriptive and inferential statistics. Descriptive statistics are used to describe characteristics of a whole population, while inferential statistics are used when the whole population cannot be measured and conclusions are drawn from a sample to generalize to the larger population. Examples are provided to illustrate when each type of statistic would be used. Key differences include descriptive statistics examining entire populations while inferential statistics examine samples that aim to infer conclusions about populations.
Diff rel ind-fit practice - Copyright Updated
The document provides explanations and examples for different types of statistical questions:
- Difference questions compare two or more groups on an outcome.
- Relationship questions examine if a change in one variable is associated with a change in another variable.
- Independence questions determine if two variables with multiple levels are independent of each other.
- Goodness of fit questions assess how well a claim matches reality.
Examples are given for each type of question to illustrate key concepts like comparing groups, examining associations between variables, assessing independence, and evaluating how a claim fits observed data.
Normal or skewed distributions (inferential) - Copyright updated
- The document discusses determining whether distributions are normal or skewed
- A distribution is considered skewed if the skewness value divided by the standard error of skewness is less than -2 or greater than 2
- For the old car data set in the example, the skewness value of -4.26 divided by the standard error is less than -2, so this distribution is negatively skewed
- The new car data set skewness value of -1.69 divided by the standard error is between -2 and 2, so this distribution is normal
Normal or skewed distributions (descriptive both2) - Copyright updated
The document discusses normal and skewed distributions and how to identify them. It provides examples of measuring forearm circumference of golf players and IQs of cats and dogs. The forearm circumference data is normally distributed while the dog IQ data is left skewed based on the skewness statistics provided. Therefore, at least one of the distributions (dog IQs) is skewed.
Nature of the data practice - Copyright updated
The document discusses different types of data:
- Scaled data provides exact amounts like 12.5 feet or 140 miles per hour.
- Ordinal or ranked data provides comparative amounts like 1st, 2nd, 3rd place.
- Nominal data names or categorizes values like Republican or Democrat.
- Nominal proportional data are simply percentages like Republican 45% or Democrat 55%.
Nature of the data (spread) - Copyright updated
The document discusses scaled and ordinal data. Scaled data can be measured in exact amounts like distances and speeds. Ordinal data provides comparative amounts by ranking items, like the top 3 states in terms of well-being. Examples ask the reader to identify if data is scaled or ordinal, like driving speeds which are scaled, or baby weight percentiles which are ordinal as they compare weights.
Mode practice 1 - Copyright updated
The document is a series of questions and examples that explain what it means for a question to ask about the "most frequent response". It provides examples of questions asking about the highest/most number of something based on data in tables or lists. It then asks a series of questions to determine if they are asking about the most frequent/common response based on the data given.
Nature of the data (descriptive) - Copyright updated
The document discusses two types of data: scaled data and ordinal data. Scaled data can be measured in exact amounts with equal intervals between values. Ordinal or ranked data provides comparative amounts but not necessarily equal intervals. Several examples are provided to illustrate the difference, including driving speed, states ranked by well-being, and elephant weights. Practice questions are also included for the reader to determine if data examples provided are scaled or ordinal.
Dichotomous or scaled
The document discusses whether variables are dichotomous or scaled when calculating correlations. It provides examples of correlations between ACT scores and whether students attended private or public school. One example has ACT scores as a scaled variable and school type as dichotomous. Another has lower and higher ACT scores as dichotomous and school type as dichotomous. It emphasizes determining if variables are both dichotomous, or if one is dichotomous and one is scaled.
Skewed less than 30 (ties)
The document discusses the correlation between ACT scores and a measure of school belongingness. It determines that one of the variables, which has a sample size less than 30, is skewed and has many ties. As a result, a non-parametric test should be used to analyze the relationship between the two variables.
Skewed sample size less than 30
The document discusses using parametric versus non-parametric tests based on sample size for skewed distributions. For skewed distributions with a sample size less than 30, a non-parametric test is recommended. For skewed distributions with a sample size greater than or equal to 30, a parametric test is recommended. It provides examples analyzing the correlation between ACT scores and sense of school belongingness using both approaches.
Ordinal (ties)
The document discusses whether there are many ties or few/no ties within the variables of the relationship question "What is the correlation between ACT rankings (ordinal) and sense of school belongingness (scaled 1-10)?". It determines that ACT rankings, being ordinal, have many ties, while sense of school belongingness, being on a scale of 1-10, may have many or few ties depending on how scores are distributed.
Ordinal and nominal
The document discusses identifying whether variables in statistical analyses are ordinal or nominal. It provides examples of relationships between variables such as ACT rankings and sense of school belongingness, daily social media use and sense of well-being, and private/public school enrollment and sense of well-being. It asks the reader to identify if variables in examples like running speed and shoe/foot size or LSAT scores and test anxiety are ordinal or nominal.
Relationship covariates
The document discusses covariates and their impact on relationships between variables. It defines a covariate as a variable that is controlled for or eliminated from a study. It explains that if a covariate is related to one of the variables in the relationship being examined, it can impact the strength of that relationship. Examples are provided to demonstrate when a question involves a covariate or not.
Relationship nature of data
This document discusses the nature of variables in relationship questions. It can be determined that the variables are either both scaled, at least one is ordinal, or at least one is nominal. Examples of different relationship questions are provided that fall into each of these categories. The document also provides practice questions for the user to determine which category the variables fall into.
Number of variables (predictive)
The document discusses the number of variables involved in research questions. It explains that many relationship questions deal with two variables, such as gender predicting driving speed. However, some questions deal with three or more variables, for example gender and age predicting driving speed. The document asks the reader to identify whether example research questions involve two or three or more variables.
Levels of the iv
The document discusses independent and dependent variables in research questions. It provides examples to illustrate that an independent variable has at least two levels and may have more, such as religious affiliation having two levels (Western religion and Eastern religion) or company type having three levels (Company X, Company Y, Company Z). It then provides a practice example about employee satisfaction rates among morning, afternoon, and evening shifts, identifying shift status as the independent variable with three levels.
Independent variables (2)
The document discusses independent variables and how they relate to research questions. It provides examples of questions with one independent variable, two independent variables, and zero independent variables. An independent variable influences or impacts a dependent variable. Questions are presented about employee satisfaction rates, agent commissions, training proficiency, and cyberbullying incidents to illustrate different numbers of independent variables.
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Quick reminder is this a central tendency - spread - symmetry question(2)
- 1. These three question types deal with how the data in a distribution is laid out. Central Tendency Spread Symmetry Central Tendency, Spread, or Distribution Shape? Represents the point or area in the distribution of data where scores tend to predominate or cluster. Look for words like, average, mean, median, most common, center point etc. Distributions of data will tend to have a dispersion or spread of scores around the central tendency. Look for words like spread, difference, deviation, range, variation, etc. Symmetry has to do with he shape of a distribution When the distribution is symmetrical it has most of the values in the middle with equally decreasing values to the left and right of the distribution (as shown to the left). A distribution is asymmetrical when it does not follow this pattern (see the bottom two images to the left). You normally will not be asked to assess skew directly but it is an important step in determining the type of spread or central tendency statistics you will run.