Module 2

Question 1

Three measures of center for quantitative variables

Answer 1

Mean, Median, Mode

Question 2

Mean

Answer 2

Average

Question 3

Finding average / sample mean

Answer 3

(y1 + y2 + y3) divided by total number of observations –> n

Question 4

Median

Answer 4

Middle

Question 5

Finding median with odd number of observations

Answer 5

(n+1) divided by 2

Question 6

Finding median with even number observations

Answer 6

Take two middle observations:

(observation 1 + observation 2) divided by 2

Question 7

Outlier

Answer 7

Observation much smaller or greater than main body of observations

Question 8

Is the median affected by the outlier?

Answer 8

No

Question 9

Mode

Answer 9

Highest frequency

Question 10

Three quartiles and corresponding percentiles

Answer 10

Q1 –> 25%
Q2 –> 50%
Q3 –> 75%

Question 11

Five number summary

Answer 11

min, Q1, Q2, Q3, max

Question 12

Determining five number summary with odd number of observations

Answer 12

Find median –> Q2
Don’t include median when calculating Q1 and Q3

Q1 = (add two middle numbers) divided by two

Q3 = (add two middle numbers) divided by two

Find min and max

Question 13

Determining five number summary with even number of observations

Answer 13

Find median –> Q2
Include median when calculating Q1 and Q3

Q1 = (add two middle numbers) divided by two

Q3 = (add two middle numbers) divided by two

Find min and max

Question 14

Frequency

Answer 14

Number of observations

Question 15

Calculating relative frequency / proportion

Answer 15

Frequency divided by frequency total

Question 16

Marginal distribution

Answer 16

Totals of each frequency distribution

Question 17

Response variable (y)

Answer 17

Main variable
Explained by or depends on explanatory variable (x)

Question 18

To get joint distribution from contingency table

Answer 18

Divide options by overall total then multiply by 100 to get percent

Question 19

When to use joint distribution

Answer 19

When sentence says
“and”

Question 20

When to use conditional distribution

Answer 20

When sentence mentions particular group

Question 21

Three measures of spread for quantitative variables

Answer 21

Range, IQR, standard deviation (SD)

Question 22

IQR

Answer 22

Difference between Q3 and Q1

Q3 - Q1

Question 23

How to determine outliers

Answer 23

Upper fence = Q3 + 1.5 x IQR

Lower fence = Q1 - 1.5 x IQR

Outlier if higher than upper fence and lower than lower fence

Question 24

Range

Answer 24

Largest - smallest

Question 25

Population mean symbol and calculation

Answer 25

μ (mu) Sum of values divided by total population size (n)

Question 26

Sample mean symbol and calculation

Answer 26

ȳ (y bar) Sum of values divided by total sample size (n)

Question 27

Population standard deviation symbol and calculation

Answer 27

σ (sigma) Find population variance Square root population variance

Question 28

Sample standard deviation symbol and calculation

Answer 28

s Find sample variance Square root sample variance

Question 29

Population variance symbol and calculation

Answer 29

σ² 1. Find μ 2. Subtract μ from each data point 3. Square answers from step 2 4. Add all answers from step 3 5. Divide step 4 answer by n

Question 30

Sample variance symbol and calculation

Answer 30

s² 1. Find ȳ 2. Subtract ȳ from each data point 3. Square answers from step 2 4. Add all answers from step 3 5. Divide step 4 answer by n-1

Question 31

Does standard deviation have same unit as original data?

Answer 31

Yes

Question 32

When is standard deviation zero?

Answer 32

No variance in data (all data is the same value)

Question 33

When to use density and how to calculate it

Answer 33

Use when intervals have different lengths Relative frequency divided by length of interval / BINS

Question 34

What does ( and ] mean for BINS?

Answer 34

( --> include that number and any number greater ] --> go up to that number but don't include the number itself

Question 35

How to describe histogram

Answer 35

Shape --> number of humps / mods --> symmetric or skewed --> outliers Center --> mean, median, mode Spread --> range, SD, IQR

Question 36

What type of distribution is a graph with no mods, one mod, two mods, and more than two mods?

Answer 36

Uniform --> no mods Uni-modal --> one mode Bimodal --> two mods Multimodal --> more than two mods

Question 37

Describe what a graph looks like when symmetric and skewed left and right

Answer 37

Symmetric --> same shape reflected on both sides of center Left skewed --> highest mod on right --> tail on left Right skewed --> highest mod on left --> tail on right

Question 38

What to use when measuring center and spread of histogram when histogram is skewed

Answer 38

Median --> center SD --> spread

Question 39

What to use when measuring center and spread of histogram when histogram is symmetric

Answer 39

Mean --> center IQR --> spread

Question 40

Order mean, mode, median least to greatest on right skewed histogram

Answer 40

Mode < Median < Mean

Question 41

Order mean, mode, median least to greatest on left skewed histogram

Answer 41

Mean < Median < Mode

Question 42

Box plot when symmetric

Answer 42

Q2 in the middle of Q3 and Q1 Max and min whiskers are same length

Question 43

Box plot when right skewed

Answer 43

Q2 closer to Q1 Max whisker longer than min whisker

Question 44

Box plot when left skewed

Answer 44

Q2 closer to Q3 Min whisker longer than max whisker