Descriptive Statistics, Introduction to Probability

Question 1

Descriptive Statistics?

Answer 1

• numbers used to describe the data collected

- 5-10% of statistics

Question 2

Statistic?

Answer 2

• descriptive measure from a SAMPLE

Question 3

Mean of a sample (statistic) and the number of observations in the sample variable?

Answer 3

mean= x-bar (bar over top of x)
# of observations in a sample= n

Question 4

Parameter?

Answer 4

-descriptive measure computed from a population

Question 5

Mean and # of observations in population in a parameter (population) variable?

Answer 5

mean= u
# of observations in a population= N

Question 6

Measures of Central Tendency?

3 measures of it?

Answer 6

• convey info regarding the average, midpoint and most common value collected in a. data set
• mean, median and mode

Question 7

Measures of Dispersion?

Answer 7

• 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

Question 8

Mean?

Answer 8

-Sum/ average

Question 9

Subscript of “x” for finding the mean

Answer 9

• subscript just lists the different pieces of data

Question 10

3 properties of mean?

Answer 10

1. unique (can only be one)
2. simplicity (easy to find)
3. affected by extreme values

Question 11

Median?

median with an even numbered set?

Answer 11

• 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

Question 12

(n+1)/2th is the equation for finding the?

Answer 12

• median

- points to a location in a data set where you will find the median value

Question 13

Mode?

Answer 13

• value in a data set that occurs most frequently

Question 14

3 properties of the median?

Answer 14

1. uniqueness
2. simplicity
3. NOT affected by outliers/ extreme values

Question 15

Is there dispersion if all the value sin a data set are the same?

Answer 15

No

Question 16

Range?

Answer 16

• difference b/w the highest value and lowest value in a data set
• effected by extreme values
• doesn’t use all the data pieces in a data set

Question 17

Q1? Q2? Q3? (what are their percentiles?)

Answer 17

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)

Question 18

Interquartile Range (IQR)?

Answer 18

IQR= Q3-Q1

-difference between the first and third quartiles that make up the middle 50% of the data

Question 19

Data Skewness?

Answer 19

• 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

Question 20

+ or - if a graph is skewed to the left? right?

Answer 20

skewed left= negative

skewed right= positive

Question 21

Negatively Skewed value)median v?

Answer 21

• median value is to the left of the peak of the graph

mean, median then mode [at the peak]

Question 22

Positively Skewed (median value)?

Answer 22

• median value is to the right of the peak

- Mode[peak], median then the mean

Question 23

In a symmetric distribution, where does the mean, median and mode lie?

Answer 23

• centre, around the peak of the graph

Question 24

Variance?

Answer 24

• amount of spread around the mean value

-

Question 25

Standard Deviation?

Answer 25

• a quantity calculated to indicate the extent of deviation for a group as a whole.
• variance squared

Question 26

A measure of dispersion tells us…?

Answer 26

-how well the measure of central tendency represents the entire data set

Question 27

Probability?

Answer 27

• measure of uncertainty

- measurement of the likelihood of an event occuring

Question 28

P-values?

Answer 28

-probability from a normal distribution
central to inferential statistics
-refers to the probability of getting a result by chance alone

Question 29

Empirical Probability?

Answer 29

• likelihood of events inferred by collecting data

- probability comes from data collected

Question 30

Theoretical Probability?

Answer 30

• non data needed

- theory will tell you the probability

Question 31

Sample Space?

Answer 31

• set of all possible results or outcomes of a study

Question 32

3 properties of probability?

Answer 32

• 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

Question 33

Mutually Exclusive?

Answer 33

-means that if you are one thing you cannot be another

Question 34

P(A)= m/N?

Answer 34

P(A)= probability of event A occurring
m= numbers rof times the event occurred
N= total number of trials

Question 35

𝐩(𝐀̅ )= 𝑚̅/𝑁?

Answer 35

𝐩(𝐀̅ )= probability that event A will not occur
𝑚̅= number of times events other than m occured
𝑁= total number of trials

Question 36

P(A|B)?

Answer 36

-probability that event A will occur given that event B has occurred
A= subset
B= what has occurred already

Question 37

P(A∩B) = P(A) x P(B|A)

Answer 37

P(A∩B)= probability that events A and B both occur

Question 38

Independent events?

Answer 38

-two events are independent when the occurrence of one does not change the probability that the other will occur

Question 39

P(A∩B) = P(A) x P(B)

Answer 39

Probability that 2 independent events occur

Question 40

Are independent event mutually exclusive?

Answer 40

No

-can co-occur but they do not depend on one another

Question 41

P(AUB) = P(A) + P(B) – P(A∩B)

Answer 41

P(AUB)= probability that event A will occur or event B will occur

Question 42

P(AUB) = P(A) + P(B)

Answer 42

-probability of A occurring or B occurring is A and B are mutually exclusive