Descriptive Statistics, Introduction to Probability Flashcards
Descriptive Statistics?
- numbers used to describe the data collected
- 5-10% of statistics
Statistic?
- descriptive measure from a SAMPLE
Mean of a sample (statistic) and the number of observations in the sample variable?
mean= x-bar (bar over top of x) # of observations in a sample= n
Parameter?
-descriptive measure computed from a population
Mean and # of observations in population in a parameter (population) variable?
mean= u # of observations in a population= N
Measures of Central Tendency?
3 measures of it?
- convey info regarding the average, midpoint and most common value collected in a. data set
- mean, median and mode
Measures of Dispersion?
- measure of the amount of spread/ how far apart the different data pieces are spread apart
- displays the measure of variability in a data set
Mean?
-Sum/ average
Subscript of βxβ for finding the mean
- subscript just lists the different pieces of data
3 properties of mean?
- unique (can only be one)
- simplicity (easy to find)
- affected by extreme values
Median?
median with an even numbered set?
- median divides the data set into two equal parts
- to find it, list the data pieces in numeric order
- find which two pieces of data are in the middle, add them and then divide by 2
(n+1)/2th is the equation for finding the?
- median
- points to a location in a data set where you will find the median value
Mode?
- value in a data set that occurs most frequently
3 properties of the median?
- uniqueness
- simplicity
- NOT affected by outliers/ extreme values
Is there dispersion if all the value sin a data set are the same?
No
Range?
- difference b/w the highest value and lowest value in a data set
- effected by extreme values
- doesnβt use all the data pieces in a data set
Q1? Q2? Q3? (what are their percentiles?)
Q1= 25% of participants fall bellow this value (75 above) Q2= 50% of participants fall bellow this value Q3= 75% of values fall below this value (25 above)
Interquartile Range (IQR)?
IQR= Q3-Q1
-difference between the first and third quartiles that make up the middle 50% of the data
Data Skewness?
- data can be classified whether it is symmetric or asymmetric
- if symmetric, the left half and right half of a histogram frequency polygon are mirror images
+ or - if a graph is skewed to the left? right?
skewed left= negative
skewed right= positive
Negatively Skewed value)median v?
- median value is to the left of the peak of the graph
mean, median then mode [at the peak]
Positively Skewed (median value)?
- median value is to the right of the peak
- Mode[peak], median then the mean
In a symmetric distribution, where does the mean, median and mode lie?
- centre, around the peak of the graph
Variance?
- amount of spread around the mean value
-
Standard Deviation?
- a quantity calculated to indicate the extent of deviation for a group as a whole.
- variance squared
A measure of dispersion tells us�
-how well the measure of central tendency represents the entire data set
Probability?
- measure of uncertainty
- measurement of the likelihood of an event occuring
P-values?
-probability from a normal distribution
central to inferential statistics
-refers to the probability of getting a result by chance alone
Empirical Probability?
- likelihood of events inferred by collecting data
- probability comes from data collected
Theoretical Probability?
- non data needed
- theory will tell you the probability
Sample Space?
- set of all possible results or outcomes of a study
3 properties of probability?
- probability is always positive or zero (never negative)
- sum of all probabilities of all mutually exclusive events is equal to 1
- Probability of that event occurring is the added sum of their individual probabilities
Mutually Exclusive?
-means that if you are one thing you cannot be another
P(A)= m/N?
P(A)= probability of event A occurring m= numbers rof times the event occurred N= total number of trials
π©(πΜ )= πΜ /π?
π©(πΜ
)= probability that event A will not occur
πΜ
= number of times events other than m occured
π= total number of trials
P(A|B)?
-probability that event A will occur given that event B has occurred
A= subset
B= what has occurred already
P(Aβ©B) = P(A) x P(B|A)
P(Aβ©B)= probability that events A and B both occur
Independent events?
-two events are independent when the occurrence of one does not change the probability that the other will occur
P(Aβ©B) = P(A) x P(B)
Probability that 2 independent events occur
Are independent event mutually exclusive?
No
-can co-occur but they do not depend on one another
P(AUB) = P(A) + P(B) β P(Aβ©B)
P(AUB)= probability that event A will occur or event B will occur
P(AUB) = P(A) + P(B)
-probability of A occurring or B occurring is A and B are mutually exclusive
