Measures of Central Tendency
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Questions and Answers

What are the three most common measures of central tendency?

Mean, median, and mode

Central tendency refers to the measure that identifies the center or typical value of a data set.

True (A)

What is the mean of the following data set: 3, 7, 5, 10, 5, 9, 14, 7, 3, 5, 3, 3?

6

What is the type of data set when there is only one mode in the data set, meaning that a single value appears most frequently?

<p>Unimodal (A)</p> Signup and view all the answers

What is the type of data set when there are two modes in the data set, meaning that two different values appear with the same highest frequency?

<p>Bimodal (C)</p> Signup and view all the answers

What is the type of data set when there are more than two modes in the data set, meaning that three or more values appear with the same highest frequency?

<p>Multimodal (D)</p> Signup and view all the answers

What is the type of data set when there is no mode as no number repeats, meaning that every value appears with the same frequency?

<p>Amodal (A)</p> Signup and view all the answers

What is the simplest measure of variability?

<p>Range</p> Signup and view all the answers

What is the formula for variance?

<p>Variance = Sum of squared deviations / Number of scores</p> Signup and view all the answers

What is the formula for the mean?

<p>Mean = Sum of all scores / Number of scores</p> Signup and view all the answers

What is standard deviation?

<p>Standard deviation is the square root of the variance.</p> Signup and view all the answers

The standard deviation is the negative square root of the variance.

<p>False (B)</p> Signup and view all the answers

What is variability?

<p>Variability refers to the amount of spread of the scores around the mean in a distribution. It describes how close or far from the mean the scores are.</p> Signup and view all the answers

What are the common measures of variability?

<p>Range, Variance, and Standard Deviation</p> Signup and view all the answers

What is the difference between variance and standard deviation?

<p>Variance is calculated by averaging the squared differences from the mean while standard deviation is the square root of the variance. Standard deviation is in the same units as the data, making it easier to interpret than variance.</p> Signup and view all the answers

Flashcards

Central Tendency

A statistical measure that represents the typical or central value of a dataset.

Mean

The arithmetic average of all values in a dataset. Calculated by summing all values and dividing by the number of values.

Median

The middle value in a dataset arranged in ascending or descending order. If there's an even number of values, it's the average of the two middle values.

Mode

The value that appears most frequently in a dataset. A dataset can have one mode, multiple modes, or no mode.

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Range

The difference between the highest and lowest values in a dataset.

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Variance

A measure of how spread out the data points are from the mean. A higher value indicates more spread.

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Standard Deviation

The square root of the variance. It represents the spread of data in the same units as the original data.

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Dispersion

The process of spreading or distributing something.

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Deviation Score

A measure that describes how far each data point is from the mean.

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Sum of Squared Deviations

The sum of the squared deviation scores, calculated to find the variance.

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Unimodal

A distribution with only one mode, where one value appears most frequently.

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Bimodal

A distribution with two modes, where two values appear with the same highest frequency.

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Multimodal

A distribution with more than two modes, where three or more values appear with the same highest frequency.

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Amodal

A distribution where no value repeats, and every value appears with the same frequency. No mode exists.

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Population Variability

The measure of how a population is scattered.

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Sample Variability

The measure of how a sample is scattered.

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Sample

A subset of a population used to represent the entire group.

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Population

The entire group that is being studied.

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Probability

The probability of an event happening.

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Z-Score

A standard score that indicates how many standard deviations a data point is away from the mean.

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Normal Curve

A bell-shaped curve that represents the distribution of many naturally occurring phenomena.

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Outlier

A data point that is significantly different from other data points in a distribution.

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Frequency Distribution

A statistical method that displays data points in a symmetrical distribution.

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Summation

The sum of all values in a data set.

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Scatterplot

A type of graph that shows the relationship between two variables.

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Histogram

A type of graph that shows the distribution of a single variable.

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Probability

The likelihood of an event occurring, expressed as a fraction, decimal, or percentage.

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Statistics

The process of collecting, organizing, analyzing, and interpreting data to draw conclusions.

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Central Tendency

A measure of how closely data points cluster around the mean.

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Variability

A measure of how spread out data points are.

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Z-Score

A standard score that tells us how many standard deviations a data point is above or below the mean.

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Normal Distribution

A symmetrical bell-shaped curve that represents the distribution of many natural phenomena.

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Study Notes

Central Tendency

  • Central tendency is a statistical concept describing the center or typical value of a dataset.
  • It summarizes data by identifying the "middle" or "average" value around which data points cluster.
  • Common measures include mean, median, and mode.

Measures of Central Tendency

  • Mean (Arithmetic Average):
    • Calculated by summing all data points and dividing by the total number of data points.
    • Sensitive to extreme values (outliers).
  • Median:
    • The middle value in an ordered dataset.
    • Less sensitive to outliers than the mean.
    • If the dataset has an even number of values, the median is the average of the two middle values.
  • Mode:
    • The value that appears most frequently in a dataset.
    • A dataset can have one mode (unimodal), two modes (bimodal), more than two modes (multimodal), or no mode (amodal) if no number repeats in the dataset.

Variability

  • Variability describes the spread or dispersion of scores around the mean in a distribution.
  • It indicates how close or far from the mean the scores are.
  • Variability, also called dispersion, helps assess the consistency or diversity of the data.

Measures of Variability

  • Range:
    • Simplest measure of variability.
    • Calculated as the difference between the highest and lowest values in a dataset.
    • Formula: Range = Maximum Value - Minimum Value
  • Variance:
    • Measures the average squared deviation of each data point from the mean.
    • Reflects how spread out the data is from the mean.
    • Formula involves subtracting the mean from each score, squaring the differences (deviation scores), summing those squares, and dividing by the number of scores.
  • Standard Deviation:
    • The square root of the variance.
    • Provides a measure of spread in the same units as the data, making it more interpretable.
    • Calculated as (Variance)^0.5

Additional Concepts

  • Σ (Sigma): The capital Greek letter sigma, used in statistics as a symbol to indicate the sum of.
  • X: Represents the scores in a data distribution. Or one variable in an equation.
  • M/X̄: The symbols used to represent the mean of data.

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Psychology Statistics Chapter 2 PDF

Description

This quiz covers the fundamental statistical concept of central tendency, including definitions and calculations for mean, median, and mode. Explore how these measures provide insights into the typical values within a dataset and their sensitivity to outliers. Test your understanding of how variability impacts data distribution.

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