Download Ultimate test 1 study guide Chapter 1 1.1 Def Def Descriptive stat

Ultimate test 1 study guide
Chapter 1
1.1 Def
Def
Descriptive stat-consists of organizing and summarizing the information collected
Inferential stat- uses methods that take results obtained from a sample, extends them to the
population, and measure the reliability of the result
Qualitative variable- allow for classification of individuals on some attribute or characteristic
Quantitative variable- provide numerical measures of individuals
Discrete value- quantitative variable that has either a finite number or possible values or a
countable number of possible values
Continuous variable- is a quantitave variable that has an infinite number of possible values that
are not countable
Population-group being studied
Individual- person or object in a population
Sample- subset of a population
1.2 Sampling
PART 1 DEF AND CONCEPTS
Census- list of all individuals in a population along with certain characteristics of each individual
Observational study- measures the characteristics of a population by studying individuals in a
sample but does not manipulate or influence the variable
Designed experiment- applies a treatment to individuals, experimental units
PART 2 RANDOM SAMPLES
 Most basic sample survey is simple random sampling
n= donates sample size of population
1.3 Sampling Methods
Stratified sample-obtained by separating the population into non-overlapping groups called strata
then obtaining a sample from each strata
Systematic sample- obtained by selecting every kth individual from a population.
Chapter 2
Descriptive Stat
2.1 Organizing data
Relative frequency- the proportion (or percent) of observations within a category
 Formula= relative frequency= frequency/ sum of all frequencies
 Ex. Find the relative frequency of the always category
Response
Frequency

Never

25

Always

98

sometimes

12
Step 1: get total of frequency= 25+98+12=135
Step 2:plug in and solve= 98/135=.7259
Types of charts
Bar graph- graph with bars, category on horizontal axis and frequency on vertical axis
Pareto- bar graph with values from highest to lowest
Pie chart- obvious
2.2 organizing data
Histogram- constructed by drawing rectangles for each class of data, height of each rectangle is
the frequency or relative frequency of the class. Width of each rectangle is the same and the
rectangles touch each other
Shapes of histograms symmetrical- even on both sides
 skewed left- shifts toward right (mean<median)
 skewed right-shifts toward left( mean> median)
Stem and leaf plot-another way to represent quantitative data, made from a stem part and a leaf
part
Terms to remember:
Size=number of observations
Location=mean, median, mode
Spread- range, variance, standard deviation
Parameter- a summary number for a population
 a constant
Statistic- summary for a sample
 variable
Mean Median Mode
Mean= average: formula
Median- middle
Mode- most frequent
If I say “median” you say “index position value”
Range= max- min
Sum of squares: table to define variance
Finding variance and standard deviation.
Variance-average of squared deviations of the data points from their mean.
Formula:
X= data
M= average
n-1= degrees of freedom. How many categories you have – 1.
Ex. What is the sum of squares of the data
22,23,19,28
M=mean=92/4
i
x
1
22
2
23
3
19
4
28
x-M
22-23=-1
23-23=0
19-23=-4
28-23=5
(x-M)^2
1
0
16
25
So sum of squares = 1+0+16+25=42
Variance= sos/ degrees of freedom
So 42/ n-1 or 42/ 4-1
= 42/3
= 14
Finding standard deviation
Std= square root of variance
Ex. Find standard deviation from above data set
Take square root of 14= 3.74
Finding quartile ranges
Median is the 50th percentile
First quartile= number so that 25% is smaller and 75% are greater
Third quartile= number so that 75% are smaller and 25 % greater
Interquartile range= difference between 3rd and 1st quartile
Q3-Q1= IQR
Five Number Summaries
=
(min, Q1, median, Q3, max)
Finding quartiles
Steps for Q1= (25/100) x number of data +1
Q3=(75/100) X number of data + 1
Boxplot= a graph of the 5 number summary
Shape
Median
Tail
Symmetric
Skewed right
Skewed left
Center of box
Left of center
Right of center
Lower fence =Q1- 1.5(IQR)
Upper fence=Q3+1.5(IQR)
Chapter 3
Probability= area under curve
Z scores
Population z score
Z= (x- population mean)/population standard deviation
Sample z score
Z= (x- mean)/ standard deviation
Ex. Find z score
Mean= 40
Population std= 11
What is the z score for 82?
(82- 40)/ 11=3.818
STANDARD NORMAL CURVE
Equal in length
Right tail is longer
Left tail is longer
Finding z scores and areas
Finding area to the right of a positive z score= located z score on table and use that point
Ex. Find are to the right of z= +1.00
= 0.1587
Finding area to the right of a negative z score= locate z score on table then subtract point from 1
Ex. Find area to right of z=-1.25
= 1- .1056= .8944
Finding area to the left of a negative z score= locate z score on table then use point
Finding area to the left of a positive z score = locate z score then 1 – point found
For finding the lower and middle z scores of an area
 if the area is above .5 then subtract it from one.
 Next, take that answer and divide by 2, this gives you an upper and lower portion
 Now locate that half area on the chart and take the positive and negative identical z scores
Finding x from z score formula
Again formula:
Z= (x- mean)/ standard deviation
So now make it x= mean +z(standard deviation)
Ex. Quiz 4 B
4B. Prob that 1Q below 110?
Set up z formula




Z= 110-100/ 16= .62 now find .62 z score and get the area.
You will get .2676, but since you want below 110 this means the left tail
This means that you are using a positive z score from the left, so subtract .2676 from 1
This gives you your answer of .7324
4A. Percent of people above 132
 Use formula and set up
 132-100/16= 2
 Now since it is a posisitve z score from the right hence above 132 you find the area of z
score 2
 Now you get .0228
 Now to get that to a percent multiple by 100
 You get 2.28 %
4C Prob of IQ between 90 and 120
 You must set up the z formula twice
 For 90= 90-100/ 16= -0.625, since it’s a negative z score from the left as 90 <100
(median) you just use the are found at -.625 z score, which is .2643
 For 120= 120-100/16=1.25 since it’s a positive z score from the right you find the area of
1.25 z score which is .1151
 Now take those add them together then subtract them from 1
4D Find IQ that separates from top 3% and bottom 97%
 Look at it in this fashion the top stands for right tail and bottom is left tail
 Since 97% would be .97 that is to large so we shall just use .03 for 3% as our area
 This allows you to find .0301 on the table with a z score of 1.88
 Now take this 1.88 and plug in to the formula
 1.88= x- 100/ 16

30.08 = x-100

130. 08 = x

130.08 rounds to 130 your answer
4E The middle 50% falls between which lower and upper IQ scores?
 Since the middle is 50% you need two tails so you divide by two giving you 25%
 This gives you .25 area, then you locate a z score for this and plug into formula
 You use .25 to find .67 and - .67 z scores
 Now set up for both,
 .67= x-100/16
 10.72= x-100




110.72= x, 111 = x
Now, -.67=x-100/16
-10.72=x-100
89.28= x and it rounds to 89
Always use percents as areas not z scores
For section 3 on quiz 1B
Notes if area is greater than .5 then subtract it from one and use that are