Terms and Definition
What is variability?
How the scores are scattered around the central point
How much scores in a dataset differ from each other
Compute the range:
[3, 9, 4, 10, 18, 15, 5, 24, 18, 7, 12, 22]
V1: 21
V2: [3 - 24] (3 to 24)
What is M or x̄?
Mean of the sample
What does a z-score of 0 indicate?
The X value is equivalent to the mean
What are the three most common techniques for measuring central tendency?
Mean, median, and mode
What is the degree of freedom?
Accounts for the fact that sample variance will typically underestimate population variance
- Used to inflate the estimate of variance
- n - 1
Compute the mode:
[2, 12, 8, 10, 18, 8, 4, 14, 8, 7, 12, 15]
[2, 4, 7, 8, 8, 8, 10, 12, 12, 14, 15, 18]
8
What is s?
Standard deviation of the sample
What is the advantage of using z-scores to compare populations?
Provides information on whether the X value is low, average, or high depending on the populations' mean and standard deviation
- Allows you to compare distributions with different scales
What is the confidence percentage for z-scores of +/- 2.00?
95.8% or 96%
What are z-scores?
A way to express data in terms of the mean and standard deviation
Compute the median:
[1, 9, 5, 15, 18, 14, 8, 24, 18, 4, 12, 0]
[0, 1, 4, 5, 8, 9, 12, 14, 15, 18, 18, 24]
10.5
What is μ?
Mean of the population
Calculate the X-value:
M = 40, σ = 15, z = +2.00
X = 70
What is the most common measure of variability?
Standard deviation
Less common ones are range or the variance (all measures distance)
What is standard deviation?
A useful way to measure variability
Compute the mean:
[12, 27, 3, 19, 8, 25, 6, 14, 30, 1, 22, 9]
14.67 (14.666667)
What is σ?
Standard deviation of the population
Calculate the z-score:
M = 80, σ = 5, X = 60
z = -4.00
What does standard deviation measure?
Measures the “average” distance from the mean for scores in a dataset.
What is the central tendency?
A statistical measure that uses a single value to describe the center of the distribution.
- Goal is to identify the single value that best represents the entire dataset.
- Can condense a large set of data into a single value.
- Condenses a large set of data into a single value
- Descriptive statistic -> describes a set of data in a simple, concise form.
- Possible to compare two (or more) sets of data by comparing the average score.
Compute the range, mode, median, and mean:
[15, 23, 7, 32, 15, 4, 7, 10, 2, 7, 15, 13]
Then tell me what type of distribution it is.
[2, 4, 7, 7, 7, 10, 13, 15, 15, 15, 23, 32]
Range: 30 or [2 - 32]
Mode: 7 and 15
Median: 11.5
Mean: 12.5
Bimodal
What is the standard deviation equation?
The square root of variance: ∑(X-M)2 divided by (n or N)
A researcher gives two participants an anxiety test. This anxiety test has a mean of 68 and a standard deviation of 12. The researcher decides to use z-scores to simplify the distribution and then alter it so that the mean is 50 and the standard deviation is 15.
Artemis' raw score = 62
Zenn's raw score = 86
Artemis: z = -0.50(original) X = 42.5(standardized)
Zenn: z = +1.50(original) X = 72.5(standardized)
When does the mean not provide a representative value?
- When a distribution contains:
- a few extreme scores (like US income)
- or is very skewed (also like US income)
- The mean will be pulled toward the tail or toward the extreme scores.
- In this case, the mean will not provide a "central" value.
- data from a nominal scale, it is impossible to compute a mean