2.3/2.4: Variability Flashcards
Central Tendency
Summarizes the most typical values for a variable.
What are the measures for central tendency?
- mean
- median
- mode
Variability
Describes how spread out the score of a variable are.
What are the measures of variability?
- Standard deviation
- Variance
- IQR
- Range
If distributions have the same central tendency, do they have the same degrees of variability?
No, they can have different degrees of variability
What is the problem with only describing the central tendency of a distribution?
Gives an incomplete description of the data.
What are 3 types of data variability?
- Variability between different subjects
- Variability within same subjects
- Measurement error
- random and systematic
Ranges
A measure of variability that indicates how wide the distribution is
Absolute Range
Tells us the difference between the smallest and largest observed value.
What does range not consider?
Distribution shape
What is range highly susceptible to?
Outliers
Interquartile Range (IQR)
Indicates the range of the middle 50% of values, between the 25th and 75th percentile.
What does IQR tell us about the variables?
What the observations in the middle of the distribution are, without being affected by outliers (skew)
What does IQR tell us about the spread?
Where the most commonly occurring values are in a distribution (highest peak)
Box and Whisker Plots
Graph the median with IQR and range, which visualizes central tendency and variability together.
What make box and whisker plots better for comparing distributions?
When combining them with dot plots
How can variability also be conceptualized?
With deviations
Deviations
How much each data point deviates from the mean
What does it mean when there is a greater deviation of values from the mean?
- Greater spread of scores
= Greater variability
What does a value of 0 in a histogram of deviation mean?
Indicates a score that is the same as the mean of raw scores.
Negative Deviation
Most scores are less than the mean
Positive Deviation
Most scores are greater than the mean.
What should the total negative and positive deviation equal in a normal dstribution?
0
How do you quantify the amount of deviation?
- Find absolute value of all deviation scores
- Use the Mean Absolute Deviation (M.A.D)
Mean Absolute Deviation (M.A.D)
Quantify the mean of the absolute deviation
What does a larger MAD score indicate?
Distributions with a greater spread of scores.
Taking the mean of the raw deviation scores
for a variable gives you:
A. sum of squares
B. a mean of zero
C. the mean absolute deviation
D. a measure of the range of the data
Mean of zero
- Positive and negative deviations cancel out
What is the Sum of Squares?
The sum of the squared standard deviation values.
What is the formula for finding the sum of squares?
- Find the individual score values squared.
- Add the squared individual score values.
- Subtract the sum by the (sum of individual scores squared) by the number of scores in the data set.
What are the characteristics of population variables?
- Cannot be measured carefully
- Predicted with statistics
- Values are inferred from smaller samples
What are the characteristics of sample variables?
- The sample estimates are what we measure.
- The values are ideal if the sample estimate is a good estimate of the population.
- Some adjustments are needed for accurate estimates.
What are the symbols used for sample and population mean?
Sample: 𝑋-Bar
Population: μ
Variance
Gives you an estimate of the average sum of squares
How do you find the variance for a population sample?
Divide the sum of squares by the number of data values.
What is the result of finding the variance of your population data?
You get the population parameter of variance for your data
How do you find the variance of a sample population?
Sum of squares divided by (n-1)
What does dividing by (n-1) do to the estimate of sample variance?
It will be higher because you than the population estimate because you are dividing by a smaller number.
What is (n-1) also known as?
Degrees of Freedom
Degrees of Freedom
The number of values that are truly free to vary in a sample.
What sample size will the degrees of freedom have a larger impact on?
Smaller samples
How do you find the population standard deviation?
Square the (sum of squares) divided by (total number of data values)
How do you find the sample standard deviation?
Square the (sum of squares) divided b (n-1)
When are sample standard deviations used?
When you measure from a sample to learn about a larger population
When is the population standard deviation used?
If we can measure the true population mean
What are the symbols of variance for sample and population?
Sample: s^2
Population: 𝝈^2
What are the symbols of standard deviation for sample and population?
Sample: s
Population: 𝝈
Which measure of variability is in the same
units of the original variable?
A. sum of squares
B. variance
C. standard deviation
D. sum of squared deviations
Standard Deviation
-Squaring the sum of squares makes the values back to normal.
