# Stats Exam 1

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1. Element
Entity upon which data are collected on

Ex: Name of player
2. Observation
set of measurements obtained for a particular element
3. Variable
characteristic of an element
4. Variable

Categorical (qualitative)
non numerical data that is classified into categories

Ex: Position or team
5. Variable:
Categorical:

Nominal
categorical data which have no meaningful order

Ex: position, team
6. Variable:
Categorical:

Ordinal
categorical data which can be ordered.

Ex: shirt size – small, medium, large
7. Variable:

Quantitative
numerical data that is measures on a numerical scale

Ex: Points scored in a game
8. Variable:
Quantitative:

Interval
numerical data that has no true 0 point

Ex: Temperature
9. Variable:
Quantitative:

Ratio
numerical data with a true 0 point

Ex: points scored
10. Cross Sectional Data
data that is collected at the same time

Ex: points scored in a specific week
11. Time Series
data collected over different time periods

Ex: points scored over multiple seasons
12. Descriptive Statistics
uses tables, graphs, and numerical methods to summarize data
13. Inferential Statistics
uses data from a sample to make estimates or test hypotheses about the characteristics of a population
14. Population
the set of ALL elements in a population
15. Sample
a SUBSET of a population. Sample estimates a population
16. Frequency Distribution
table that summarizes the number of items that occur in non-overlapping categories
17. Histogram
graphical way to display quantitative data. Uses intervals to display frequency table data
18. Correlation
shows an association between 2 variables
19. Measures of Central Tendency

Mean
the average of a sample of (n) observations.

The mean is sensitive to extreme values
20. Measures of Central Tendency

Median
the middle point where exactly ½ of the observations on either side of that point

The median is resistant to extreme values
21. Measures of Central Tendency

Mode
the observation that occurs most frequently.

Can have 2 modes (bimodal)

or more than 2 modes (multimodal)
22. Statistic
the numeric measure of SAMPLE data
23. Parameter
the numeric measure of POPULATION data
24. Types of Distribution

Symmetric
mean = median
25. Types of Distribution

Skewed Right (positive)
median is best measure

Mean is greater than the median
26. Types of Distribution

Skewed Left (negative)
median is best measure.

Mean is less than median
27. Types of Distribution

Percentile
a data value that has at least p% fall at or below a percent value
28. To find percentile
o Arrange observations in increasing order

o Compute the index: I = (p/100)*n

o If the index (i) is an integer, then take the average of that point and the next increasing point

o If the index (i) is not an integer, use the location of the next integer greater than i
29. Quartile Range
the area between the 25th and 75th percentile. Holds 50% of the data set
30. Measures of Variability and Dispersion

Range
the difference between the largest and smallest values in a data set
31. Measures of Variability and Dispersion

Variance
based on the difference between each value and the mean

Population variance (σ2)

• Sample variance (s2)
• has (n-1) in the denominator
32. Measures of Variability and Dispersion

Standard Deviation
the square root of variance.

Easier to interpret than variance because it isin the same units as the original data
33. Measures of Variability and Dispersion

Coefficient of variation
measures how large the standard deviation is relative to the mean.

It is expressed in a percentage.

• (CV = standard deviation/mean *100).
• Lower Lower is better.

Used to compare data which has different Standard deviations and means.
34. Measures of Distribution Shape and Relative Location

Z Scores
gives the number of standard deviations an observation is from the mean.

A z score of 0 indicates that the value is equal to the mean.
35. Measures of Distribution Shape and Relative Location

Outliers
z scores greater than 2 in highly skewed distributions or greater than 3 in normal distributions
36. Measures of Distribution Shape and Relative Location

Chebyshev’s Theorem
Within +/- 2 standard deviations, 75% of the observations will fall within this range

Within +/- 3 standard deviations, 89% of the observations will fall within this range
37. Measures of Distribution Shape and Relative Location

Empirical Rule (normal distribution)
Within +/- 1 standard deviations, 68% of the observations will fall within this range

Within +/- 2 standard deviations, 95% of the observations will fall within this range

Within +/- 3 standard deviations, 100% of the observations will fall within this range
38. Measures of Distribution Shape and Relative Location

Correlation Coefficient
the relationship between 2 random variables
39. Measures of Distribution Shape and Relative Location

Correlation Coefficient

Univariate
data collected on one random variable
40. Measures of Distribution Shape and Relative Location

Correlation Coefficient

Bivariate
data collected on two random variables
41. Measures of Distribution Shape and Relative Location

Correlation Coefficient

Person product moment sample correlation coefficient
measures the strength of the linear relationship (Rxy).

The sign depends on the slope of the data.

Must fall between -1 and +1.

• This is a POINT measurement.
• 0.00 – 0.29
• Little if any correlation

• 0.30 – 0.49
• Weak/Low correlation

• 0.50 – 0.69
• Moderate correlation

• 0.70 – 0.89
• Strong/High correlation

• 0.90 – 1.00
• Very strong/very high correlation
42. Probability

Experimental Outcome
A sample point
43. Probability

Event
one or more sample points/experimental outcomes
44. Probability

Properties
The sum of the probabilities must equal 1

Probabilities must fall between 0 and 1
45. Probablities

When to use combination or permutation formula?
Combination when order is not importants (C)

Permutations when order is important (P)
46. Probabilities

Methods (3)
Classical - # of outcomes / total # of outcomes

Relative Frequency – used when an experiment is repeated many times

Subjective – based on experience or intuition. Used when no relative data is available
47. Probablities

Events
a collection of sample points/experimental outcomes ( has one or more sample points)
48. Discrete Probability Variables

Random Variables
a variable that associates a numerical value with each outcome
49. Discrete Probability Variables

Random Variables

Discrete
a finite number of values

50. Discrete Probability Variables

Random Variables

Discrete Properties
0 < f(x) < 1

Σf(x) = 1
51. Discrete Probability Variables

Random Variables

Discrete uniform probability has the form of?
f(x) = 1/n
52. Discrete Probability Variables

Random Variables

Discrete

Expected Value
the mean of a discrete random variable
53. Discrete Probability Variables

Random Variables

Continuous
numerical value in one or more intervals on the real number line.

Can pick 2 points and can find a 3rd between them such as a time measurement.

### Card Set Information

 Author: Anonymous ID: 66486 Filename: Stats Exam 1 Updated: 2011-02-15 18:27:13 Tags: Stats Folders: Description: Stats Exam 1 Show Answers:

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