Chapter 1: Intro to statistics

Question 1

What are cases, variables, and labels ?

Answer 1

Cases are the objects described by the data. Variable is a characteristic of case. Labels are special variables which distinguish between cases e.g. name of song.

Question 2

What are types of variables ?

Answer 2

Categorical: places cases in categories or groups. Continuous/quantitative has numerical value for which arithmatic operations can be performed.

Distribution of variable tells us WHAT VALUE variable takes & HOW OFTEN it takes each value.

Categorical: bar graph and pie chart (% required to make up whole pie, all cate must be included, less flexible)

Continuous: histograms, stemplots, timeplots

stemplot: all but final (rightmost) digit is stem, leaf are all final digits, put leaves in ascending order

Question 3

Bar graph vs histogram

Answer 3

Bar graph gives the no. of cases in each categorical variables. There can be space between 2 bars.
Histogram gives the DISTRIBUTION of counts between single continuous variable which is subdivided into numerical classes. Cannot be space unless the frequency is 0.

Question 4

Overall pattern of distribution

Answer 4

Shape (symmetry, unimodal, right-left skewed), center, spread (max-min value, outlier)

Question 5

Right-skewed

Answer 5

Right side OF THE GRAPH (containing half of the observations and larger values) is longer than it’s left side

Question 6

mean vs median

Answer 6

Give us center
Mean is average, sensitive to outliers
Median is the mid-pt (half values larger the other half smaller), resistant to outlier
odd: middle no.
even: average of 2 middle nos.

Question 7

Spread

Answer 7

Can be given by:
1) Quartiles: Q1,Q2,Q3
Q1 is the median of obs to left of media
Q3 is the median of obs to the right of media
Q2=median
IQR=Q3-Q1
2) Five Number summary: Min Q1 M Q3 Max
Can be indicated by box plot. The whiskers extending from box give min and max values (THAT ARE NOT OUTLIERS).
3) 1.5IQR: Q1-1.5IQR, value below this is outlier
1.5IQR: Q1+1.5IQR,value above this is an outlier
4) Standard deviation (s):
obs-mean: devaition
average of square root of all deviations: variance (s2)
square root of variance is SD
But average done by n-1: degrees of freedom
USED only when MEAN is measure of center
SENSITIVE to outliers like mean , more bcuz of square root
s=0 when all values same i.e. no spread
SD preferred over Variance as UNITS same as OBS

Question 8

Measure of center and spread

Answer 8

Use mean and SD only for symmetric distri as sensitive to outliers
For skewed distributions use median and quartiles

Question 9

Linear transformation of variables

Answer 9

xnew=a +bx; x:obs
1) b multiplies center (mean, median) as well as spread(SD,IQR)
2) “a” adds to the center (mean, median) but NOT to the spread (SD,IQR) i.e. remains same

BUT OVERALL SPREAD and CENTER does not change by linear transformation

Question 10

Density Curve

Answer 10

• Histogram, smooth curve over it, make AUC=1 (proportion), always above or on hori axis
• Outliers not described
• Median: divides curve in half
• Mean: Balance-pt
• Actual obs: x-bar and s; density curve: mu and sigma

Question 11

Normal distribution and Normal density curve

Answer 11

• Distribution that has shape: symmetric, unimodal and bell-shaped
• It’s density curve is NORMAL density curve
• N(mu, sigma)
• Mean=median and it is the measure of center as it is a symmetric distribution
• If mu changed then the curve moves to right or left but spread stays same
• Spread determined by sigma

Question 12

68-95-99.7 Rule

Answer 12

68% of obs fall within sigma of mu, 95% with 2sigma and 99.7% within 3sigma of mu
CHECKOUT SUMS

Question 13

Standard Normal Distribution

Answer 13

• Variable x has a “z-score/standardized-value”=x-u/sigma
• This is standard normal distri
• Always has N(0,1)
• CHECKOUT SUMS
• Would be with center 0 and 3 posi/nega SD on each side (acc to 68-95-99.7 rule)

Question 14

Standard Normal Table

Answer 14

AUC to the left of each z value
-3.4 to 3.4
SOLVE SUMS