Stats Exam 1

Entity upon which data are collected on

Ex: Name of player

set of measurements obtained for a particular element

characteristic of an element

non numerical data that is classified into categories

Ex: Position or team

categorical data which have no meaningful order

Ex: position, team

categorical data which can be ordered.

Ex: shirt size – small, medium, large

numerical data that is measures on a numerical scale

Ex: Points scored in a game

numerical data that has no true 0 point

Ex: Temperature

numerical data with a true 0 point

Ex: points scored

data that is collected at the same time

Ex: points scored in a specific week

data collected over different time periods

Ex: points scored over multiple seasons

uses tables, graphs, and numerical methods to summarize data

uses data from a sample to make estimates or test hypotheses about the characteristics of a population

the set of ALL elements in a population

a SUBSET of a population. Sample estimates a population

table that summarizes the number of items that occur in non-overlapping categories

graphical way to display quantitative data. Uses intervals to display frequency table data

shows an association between 2 variables

the average of a sample of (n) observations.

The mean is sensitive to extreme values

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

The median is resistant to extreme values

the observation that occurs most frequently.

Can have 2 modes (bimodal)

or more than 2 modes (multimodal)

the numeric measure of SAMPLE data

the numeric measure of POPULATION data

mean = median

median is best measure

Mean is greater than the median

median is best measure.

Mean is less than median

a data value that has at least p% fall at or below a percent value

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

the area between the 25th and 75th percentile. Holds 50% of the data set

the difference between the largest and smallest values in a data set

based on the difference between each value and the mean

Population variance (σ2)

• Sample variance (s2)
• has (n-1) in the denominator

the square root of variance.

Easier to interpret than variance because it isin the same units as the original data

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.

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.

z scores greater than 2 in highly skewed distributions or greater than 3 in normal distributions

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

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

the relationship between 2 random variables

data collected on one random variable

data collected on two random variables

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

A sample point

one or more sample points/experimental outcomes

The sum of the probabilities must equal 1

Probabilities must fall between 0 and 1

Combination when order is not importants (C)

Permutations when order is important (P)

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

a collection of sample points/experimental outcomes ( has one or more sample points)

a variable that associates a numerical value with each outcome

a finite number of values

Ex: number of defective radios

0 < f(x) < 1

Σf(x) = 1

f(x) = 1/n

the mean of a discrete random variable

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.