Chapter 3 - Central Tendency Flashcards
What is central tendency?
It is the center of the distribution.
It is the single value that is most typical/representative of the collected data.
Statistics that measure the average values of data sets.
Usual measures include the mean, median, and mode.
It is a score representative of an entire distribution
What are the 3 different definitions of center in regard to central tendency?
Mean = The average score (our focus for this class)
Median = The middle score
Mode = The score that occurs most often
What is mean?
The average score
The mean evenly distributes the total amount of a variable across the sample members.
The “center of gravity” of the data set.
You find the mean by adding up all of your scores and dividing them by the number of scores you have. For example: If you have the following 6 scores 6, 12, 18, 24, 30, and 36 you’d add all of them together and divide that number by 6 (126/6 = 21). The mean is 21.
We focus on the mean in this class, applications
of the median and mode are less common in
psychological research.
You can only calculate one mean
Mean is the most sensitive to the tail of a distribution (graph) (will likely fall towards the “tail” - where the extreme values are).
You cannot calculate it for ordinal or nominal data
The mean is appropriate for numeric data ONLY (histogram/density plot/interval/ratio) and
quasi-interval (e.g., Likert) rating scales
Basically, you can ONLY use it for numerical data (ratio/interval)
What is median?
The middle score, with half of the observations smaller and half of the observations larger.
The score that divides the distribution in half
(also called the 50th percentile)
To find the middle score (median) you’ll need to:
1. Order the scores from high to low
2. Find the middle score
If two numbers share the middle you’ll need to add those two numbers together and divide them by two
You can only calculate one median
The median is the most sensitive to the “body” of a distribution (graph) (will likely be located closer to the “body” and further from the tail).
You cannot use it to calculate nominal data
Median is especially useful for ordinal variables
with binned responses (bar plot/frequency distribution) or skewed numeric data (histogram/density plot/interval/ratio)
Basically you can use it for numerical data and ordinal data ONLY
- If using a frequency table it’s best to find the median by using the cumulative percent data!
What is mode?
The mode is the score(s) that occurs most often (e.g., the peak of the distribution)
Mode is typically the highest and it’s always associated with the peak
There can be more than one mode, even two, or three modes!
To find the mode you’ll need to:
1. Order the scores from high to low
2. Find the scores that occur the most often/most frequently
3. Those scores are your mode
You can use it to calculate nominal data - actually, you can only use mode (the peak/highest point) for nominal data
You can also use it to calculate ordinal data, but the median is especially useful
Mode is especially useful for categorical variables
with qualitatively different responses.
Basically, you can use mode for EVERYTHING!!!
In a symmetric distribution, what do the mean, median, and mode equal?
Extreme scores in both tails cancel out, and the
mean, median, and mode are roughly equal.
Mean = median = mode
In a negatively skewed asymmetric distribution, what do the mean, median, and mode equal?
Mode > median > mean and each data point gets closer and closer to the left (negative) tail.
- See slide 10
In a positively skewed asymmetric distribution, what do the mean, median, and mode equal?
Mode > median > mean and each data point gets closer and closer to the right (positive) tail.
- See slide 10
True or false: Mean, median, and mode are always the same?
False
True or false: The mean is the most widely
used in psychological research, where we want to compare averages of two or more groups?
True
Behavioral scientists are concerned with
learning something about:
A: The entire population
B: The sample population
C: Both A & B
A: The entire population
What is the population mean?
The mean or average of all values in a given population.
It is calculated by the sum of all values in the population, denoted by the summation of X (the Greek capital letter, ∑ , is used to represent the sum, followed, by the letter x - so ∑x), divided by the number of population values denoted by Npop (see slide 26 for an image of the formula).
Population mean is denoted by “Mu” = μ
μ = ∑x ÷ Npop
* So basically the sum of all your data divided by the number of data points you have
This data is very hard to obtain because we almost never have access to an entire population
What is the sample mean?
It refers to the mean value of a sample of data calculated from within a large population of data.
It is calculated by the sum of all values in the sample population, denoted by the summation of X (the Greek capital letter, ∑ , is used to represent the sum, followed, by the letter x - so ∑x), divided by the number of sample population values denoted by N (see slide 26 for an image of the formula).
The sample mean is denoted by “x bar” = x̄
x̄ = ∑x ÷ N
* So basically the sum of all your data divided by the number of data points you have
What is a population?
A population is the collection of all possible
participants we are interested in studying.
Denoted by Npop - all individuals in the U.S. population
Example: All 18 years olds in the United States
- We can’t know the population mean because
populations are usually too large to study
What is a parameter?
Parameter = Population
The parameter is the value of a statistic such as
the mean computed from the full population.
It describes the whole population
The population mean is denoted by Mu = μ (mean of all data)
It’s everything related to the population (mean, median, mode, kurtosis, etc.).
- We can’t know the population mean because
populations are usually too large to study
