Measures of Central Tendency
We summarize a variable by finding a
“typical” score.
Measures of Central Tendency are
“typical” scores & represent values
around which others concentrate.
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Understanding Measures of Central Tendency & Variability: Mode, Median, Mean, Range, Varia, Lecture notes of Social Statistics and Data Analysis
An overview of measures of central tendency, including the mode, median, and mean, as well as measures of variability, such as range, variance, and standard deviation. It also discusses the importance of normal distribution and z-scores in statistics. Additionally, it covers hypothesis testing using t-tests, chi-square, and anova, as well as measures of association for ordinal level variables.
Typology: Lecture notes
2011/2012
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Measures of Central Tendency
We summarize a variable by finding a
“typical” score.
Measures of Central Tendency are
“typical” scores & represent values
around which others concentrate.
The Mode
The mode is the value with the highest
frequency count or tally.
While the mode can be useful, it only
tells us which value occurred the
most frequently…so it ignores
information on how values are
distributed.
The Mean
The mean incorporates all of the values for a variable! It is obtained by adding up all the values & dividing that sum by the total number of cases.
Since it contains the maximum information, the mean is usually the most accurate, stable & useful measure of central tendency….however, it can be distorted by a few extremely high or low values.
Measures of Variability
A quick measure is the range. To calculate ( R ), subtract the lowest value ( L ) from the highest value ( H ). It is based on the 2 extreme scores, and ignores all other information about the dispersion.
The variance reflects the sum of deviations of each value from the mean and provide us with an “average” amount of dispersion or variability.
The standard deviation is the square root of the variance.
From Descriptive to Inferential
Statistics
The “normal distribution” & z -scores
connect descriptive and inferential
statistics…by adding to the
interpretation of the mean & standard
deviation, and forming the basis for
statistical estimation, hypothesis
testing, measures of association.
Key aspects of the normal curve:
The normal curve is symmetrical or bell- shaped.
The average (mean) is also the most frequently occurring value (the mode), and the value that splits the distribution in half (the median).
Assuming a variable is normally distributed we can say more about the standard deviation.
Hypothesis Testing: t-tests