Common Definitions from Statistics 210
1. 𝜇- population mean
2. 𝜎- population standard deviation
3. σ2 –population variance
4. 𝑥̅ -Sample mean
5. 𝑠−sample standard deviation
6. s2-sample variance
7. Statistics: the science that deals with collection, classification, analysis, and
interpretation of information or data. (2 types: Inferential Statistics & Descriptive
Statistics)
8. Inferential Statistics: uses sample data to make estimates, decisions, predictions, or
other generalizations about the corresponding population. (ex. What percent of
Americans favor gun control?)
9. Descriptive Statistics: methods used to organize, describe, and display data. (this
involves using methods such as mean, median, mode, and graphs)
10. Experimental Unit: The group, member(s), or object(s) on which the data is being
collected. (Using the previous example from #2 above, Americans would be the
experimental unit)
11. Population: The set of all units that we are interested in studying (ex. Religious beliefs of
all Americans)
12. Sample: a group or subset of the population, usually randomly chosen. (ex. Religious
beliefs of 500 Americans)
Source: http://www.cliffsnotes.com/test-prep/tools-and-resources/statistics-glossary
Source: South Alabama Statistics Dept.- classroom notes from Sonna Farmer’s class
13. Parameter: A characteristic of a population, a numerical value using population data. (It
should only have one value because it being based on a population)
14. Statistic: An estimation of a population parameter, a numerical value calculated using
sample data. (It can have many values because you can draw many different random
samples from one population)
15. Variable: a characteristic of an individual experimental unit in the population (2 types)
16. Quantitative Variable: each measurement is recorded on a naturally occurring
numerical scale. (ex. ACT scores, height, # of customers today)
17. Qualitative Variable: Measurements cannot be measured on a natural scale, measured
in kind, not numerical. (ex. Color, major, these cannot be expressed simply as a
number.)
18. Representative Sample: shows traits representative of those in the target population
19. Random Sample: selected from a population in which there is no way to predict what
the outcome will be, only probabilities can be predicted.
20. Median: value of the middle term and a data set that has been ranked in increasing
order. (The median is least affected by outliers)
21. Mean: The average of the data set. ( The mean is more sensitive/more affected by
outliers, this means that an outlier is more likely to skew the mean)
22. Mode: Value in the data set that occurs with the highest frequency.
23. Variance: a measure of data variation. The population variance and sample variance are
always squared so this number will always be positive.
24. Empirical Rule: for a distribution that is mound/bell shaped and symmetric,
approximately 68% of the data values will lie within one standard deviation of the mean.
95% will lie within 2 standard deviations, and 96.7% of the data points will lie within 3
standard deviations.
25. Z-Score: tells us how many standard deviation an “x” value is from the mean and in
which direction. (ex. The “x” value is 2.5 standard deviations above the mean , it is
above the mean because the z-score is positive. A negative z-score is below the mean.
Source: http://www.cliffsnotes.com/test-prep/tools-and-resources/statistics-glossary
Source: South Alabama Statistics Dept.- classroom notes from Sonna Farmer’s class
26. Percentile: The percentile indicates that in an ordered set of data, any percentile is the
amount of data equal to and below that point. (ex. The 80 th percentile indicates that 80
percent of my data is equal to and below that mark.
27. Experiment: an act or process of observation that leads to a single outcome that cannot
be predicted with certainty.
28. Sample Point: Most basic outcome of an experiment. (ex. Flipping a coin, heads is one
sample point and tails is another)
29. Sample Space: set of all sample points of an experiment. (ex. Rolling a die {1,2,3,4,5,6})
30. Random Variable: value depends on chance (2 types)
31. Discreet Random Variable: the values can be isolated on a number line (ex. # of
customers in one day, this value is an exact number and doesn’t have a decimal point.)
32. Continuous Random Variable: the values can form a non-stop interval on a number
line. (ex. Amount of rain for the year, this number will be continuous as it rises such as
so you will have decimal points)
33. Binomial: an event with two possible outcomes
34. Sampling Distribution of the Mean: the distribution of all possible values the sample
mean can have based on the sampling process.
35. Central Limit Theorem (CLT): if a sample size is sufficiently large (more than 30 data
pts), the sampling distribution of the mean is approximately zero.
36. Hypothesis Testing: used to make a decision about the value of a population parameter
based on the value of a sample statistic.
37. Alternative Hypothesis: the hypothesis that is supported if null gets rejected, this is
what you are looking for evidence to support
38. Null Hypothesis: Directly tested by statistical analysis and confidence intervals, if null is
rejected, the alternative is accepted.
39. Type 1 error: Happens when the null hypothesis is true but it is rejected.
40. Type 2 error: Happens when the null hypothesis is false but it is not rejected.
Source: http://www.cliffsnotes.com/test-prep/tools-and-resources/statistics-glossary
Source: South Alabama Statistics Dept.- classroom notes from Sonna Farmer’s class