Chapter 4: Central Tendency and Variability Flashcards
Central Tendency
Refers to the descriptive statistic that best represents the center of a data set, the particular value that all the other data seem to be gathering around; what we mean when we refer to the “typical score”
Measures of central tendency
Mean, Median, Mode
Mean
Arithmetic average of a group of scores, often called the average, used to represent the typical score in a distribution; visual point that perfectly balances two sides of a distribution
Statistics
Numbers based on samples
Parameters
Numbers based on populations
To calculate the mean
- Add all the scores together
2. Divide the sum of all scores by the total number of scores
Median
The middle score of all the scores in a sample when the scores are arranged in ascending order
To determine the median
- Line up scores in ascending order
2. Find the middle score
Mode
The easiest measure of central tendency to calculate; it is the most common score of all the scores in a sample
Outliers and the Mean
When there is an outlier, sometimes,the mean is not representative of any one actual score especially if there is a small number of observations
The Mean without the Outlier
When the outlier is omitted, the mean may not be more representative of the actual scores in the sample
Which Measure of Central Tendency is Best
The mean is the measure of choice. However, whenever the distribution is skewed by an outlier (or when the distribution itself is skewed), the median is used to measure central tendency
Mode
Used in three situations: (1) when one particular score dominates a distribution (2) when the distribution is bimodal or multimodal (3) when the data are nominal
How to tell if you are being misled by a report of central tendency
- Notice whether it is reporting an average (mean) or a median
- If it is reporting a mean, think about whether that distribution is likely to be skewed by one extremely high number
Variability
Second most common concept used to help us understand the shape of a distribution; numerical way of describing how much spread there is in a distribution
Common indicators of variability
Range, Variance, and Standard Deviation
Range
A way to numerically describe the variability of a distribution; measure of variability calculated by subtracting the lowest score (minimum) from the highest score (the maximum)
Variance
Another way to describe the variability of a distriution
Standard Deviation
The computation of the variance and its square root
To compute Range
- Determine highest score
- Determine lowest score
- Subtract lowest score from highest score
Variance
Average of the squared deviations from the mean; describes the degree to which a distribution varies with respect to the mean
Deviation from the mean
The amount that a score in a sample differs from the mean of the sample, also called deviation
Sum of squares
Sum of each score’s squared deviation from the mean
Standard Deviation
Square root of the average of the squared deviations from the mean; typical amount each score varies, or deviates, from the mean.
Steps to compute standard deviation
- Subtract the mean from every score
- Square every deviation from the mean
- Sum all of the squared deviations
- Divide the sum of squares by the total number in the sample (N)
Interquartile Range
Measure of the distance between the first and third quartiles
First quartile
Marks the 25th percentile of a data set
Third Quartile
Marks the 75th percentile of a data set
