CH 1+CH2
What are the three types of measurement scales along with their definitions?
1. Categorical: Observations grouped into categories Examples: blood types, HIV status
2. Ordinal:Categories that can be put in a ranking order. Examples: income, stages of cancer
3. Quantitative: True numerical values that can be put on a number line (continuous). Examples: age (years), weight, blood sugar
Calculate the mean: 6.7, 7.6, 7.5, 6.9, 9.3, 6.7, 7.6, 8.5
1. add all the numbers and divide by N
7.6
Create a cumulative frequency table:
Frequency Relative frequency cumulative frequency
10
15
30
30
Frequency Relative frequency cumulative frequency
10 10 12
15 25 29
30 55 65
30 85 100
Calculate P(A or B)= P(A)=0.5, P(B)=0.3, P(A and B)=.06
(.5 + .3)- .06=.74
What are the dependent and independent variables in this scenario?
How does phone use before bedtime affect sleep?
independent: The amount of phone use before bed
dependent: Number of hours of sleep or sleep quality
FIND THE 5 POINT SUMMARY:
1 7224 8709 8784 10,060 10,089 10,125 11,445 11,476 11,844
Q0= 1
Q1=8709
Q2= 10,074.5
Q3= 11,445
Q4= 11,844
Find the 5 point summary for: 1, 7, 11, 15, 21, 32, 16
1. place numbers in order: 1, 7, 11, 16, 15, 21, 32
q0=1
q1= 9
q2= median=16
q3=18
q4= 32
What is the difference between a discrete variable and a continuous variable?
A discrete variable is a variable whose value is obtained by counting. A continuous variable is a variable whose value is obtained by measuring.
What is an observation?
The units upon which measurements are made
Example: individuals
MAKE A BOXPLOT:
(4 6 7 9 14 15 15 16 18) (18 25 26 30 32 41 45 55 63)
Q0 (minimum) - 4
Q1 - 14
Q2 - 18 (n+1)/2 (18+1)/2 = 9.5 value = 18
Q3 - 32
Q4 - 63
IQR = Q3-Q1= 32-14= 18
Lower Q1 -1.5IQR = 4 -1.5(18)= -23
Upper Q3+1.5IQR= 32+1.5(18)= 59
Lower outlier: none
Upper Outlier: 63 > 59
What is the formula for IQR and lower/upper fence?
IQR= Q3-Q1
lower fence: q1-(1.5*IQR)
upper fence:Q3+(1.5*IQR)
Calculate the varience: 1, 3, 4, 8, 9
s2 =11.5
Is the mean a resilient measure of center? Why or why not?
No it is not because it is sensitive to outliers.
FIND THE STANDARD DEVIATION OF:
371 356 393 544 326 520 501
88.7
What is the difference between disjoint and independent events?
INDEPENDENT EVENTS: Events are considered independent if they are unrelated. The occurrence of one event does not affect the occurrence of another event. Getting heads does not effect the probability of getting tails
Disjoint: they never occur at the same time; these are also known as mutually exclusive events.
A football game can’t be held at the same time as a rugby game on the same field.
What are the 4 properties of a probability function?
Property 1 (Range of possible probabilities): Individual probabilities are never less than 0 and never more than 1: 0 ≤ Pr(A) ≤ 1.
Property 2 (Total probability). Probabilities in the sample space must sum to exactly 1: Pr(S) = 1
Property 3 (Complements). The probability of a complement is equal to 1 minus the probability of the event
Property 4 (Disjoint events). Events are disjoint if they cannot exist concurrently. If A and B are disjoint, then Pr(A or B) = Pr(A) + Pr(B).
What is the median of: -7, 22, -7, 8, 16, 1
1. order the numbers
2. (N+1)/2
3. 4.5
Create a stem and leaf plot: 0.7, 1.9, 2.3, 4.3, 3.3, 5.6, 4.8, 5.2, 0.6, 0.3, 0.9
0 l 3, 6, 7, 9
1 l 9
2 l 3
3 l 3
4 l 3, 8
5 l 2, 6
x 1
What is the probability of rolling an odd number or a number less than 3 on two rolls of a 6-sided dice?
p(odd less than 3)=p(odd)+p(less than 3)-P(odd and less than 3)=(3/6 + 2/6) -⅙ =4/ 6 =⅔
Diana tossed a six-sided dice. What is the probability that she will get a 1 or a 3?
Pr( 1 or 3)= (1/6)+(1/6)= 2/6=1/3