Organizing, Visualizing, and Describing Data

Question 1

Continuous data

Answer 1

• can take on any numerical value in a specified range of values
• ex. future value

Question 2

Discrete data

Answer 2

• number has a limited number of values.

- ex. monthly = 12, quarterly = 4, etc

Question 3

Nominal data (2)

Answer 3

AKA quantitative data

• continuous
• discrete

Question 4

Categorical data (2)

Answer 4

aka qualitative data
- describe a quality or characteristic of a group of observations

• nominal data
• ordinal data

Question 5

Nominal data

Answer 5

• grouping names
• cannot be organized in a logical order
• ex. classifying stocks into different sectors, such as energy, information tech, etc

Question 6

Ordinal data

Answer 6

• can be organized in logical order or ranked
  ex. rating of mutual funds with the worst performance
• there is an order, but can’t distinguish values of magnitude

Question 7

Time-series data

Answer 7

• observations of 1 subject taken at specif and equal spaced intervals of time
  ex quarterly returns of Apple 2019-2020

Question 8

Cross-sectional data

Answer 8

• observations of multiple subjects taken at specific points in time
  ex. 2019 Q1 quarterly returns of a group of simial stocks

Question 9

Panel data

Answer 9

• presented as a table
• groups observations through time on one or more variables for multiple subjects
• quarterly returns for MSFT, Orcal, and HP from 2019 - 2020

Question 10

One-Dimensional array

Answer 10

• one row of data

- a single variable - closing price of a stock on x day

Question 11

Two-dimensional array

Answer 11

• consists of columns and rows to hold multiple variables and multiple observations
• a firm’s quarterly revenue, EPS, and DPS for past two years

Question 12

Tree-map

Answer 12

• graphical tool to display categorical data

-

Question 13

Arithmetic Mean

Answer 13

• simple mean
• the center of gravity of a data set
• sensitive to extreme values (outliers)
• appropriate for forecasting single period returns and expected returns

Question 14

Sample mean

Answer 14

• arithmetic mean of a sample
• ^x sample mean
• mue (^m) population mean

Question 15

Winsorized mean

Answer 15

• a way of dealing with outliers

- a 95% winsorized mean takes the bottom 2.5% off and the top 2.5% off

Question 16

Median of even number of observations

Answer 16

• n = 4
• 3, 9, 10, 20: take value 2&3 and add then / 2
• (9+10)/2

Question 17

Geometric Mean

Answer 17

• used to calculate the average return of an investment
• represents the growth rate of an investment
• represents the compound rate of return of an investment
• appropriate to measure past performance over multiple periods
  = [(1+r)(1+r2)(1+rn)]^1/n -1

Question 18

Harmonic mean

Answer 18

• used to find average purchase price for equal periodic investments

= n / sum of 1/xi

3 years / (1/$10) + (1 / $15) + (1/$20) = $13.85

Question 19

Relationship of Geometric mean to the arithmetic mean

Answer 19

-geo mean will always be less than arithmetic mean

Question 20

Quantiles:
quartiles, quintiles, deciles, percentiles
formula for the position of a percentile in a data set

Answer 20

4 quarters, 5 quintiles, 10 deciles, hundredths

• arrange data in ascending order (low to high)
  = Ly = (n + 1) * (y / 100)

Question 21

When to use each mean:

a. Arithmetic mean
b. Geometric mean
c. Weighted mean
d. Harmonic mean
e. Trimmed mean
f. Winsorized mean

Answer 21

a. with single period or cross-sectional data
b. with time-series data
c. when different observations have different weights
d. find avg purchase price for equal periodic investments
e. when data has extreme outliers
f. when the data has extreme outliers

Question 22

Interquartile range:

Answer 22

• the difference between the third and first quartiles

Question 23

List the Measures of Dispersion

Answer 23

• range
• Mean Absolute Deviation
• Variance (population, sample)
• Standard Deviation (population, sample)

Question 24

Range formula

Answer 24

= max value - min value

Question 25

Mean Absolute Deviation formula

Answer 25

= |xi - ^x| / n

• calculate the mean, then - each value from ^x. Total the absolute deviations and / n

Question 26

Variance

Answer 26

• population O^2
• Sample S^2
• “the average of the squared deviations around the mean”
• use cal function: 2nd, data, to solve.
• need to ^2 either the sample of population deviation

Question 27

Standard deviation

Answer 27

• “the positive square root of the variance”
• Population O
• Sample S
• use cal function: 2nd, data, to solve.

Question 28

Target deviation / target semideviation def

Answer 28

• the risk of being below a given target

- only includes the observations below the target (B)

Question 29

Target deviation / target semideviation formula

Answer 29

= sqrt root (sum squared deviations below the target / n-1)

• sqrt root ((xi - B)^2 / (n-1))
• ie if the target is 4%. find all observations < 4. Subtract observation from 4% and ^2. Sum all observations and / n - 1 then sqrt root

Question 30

Coefficient of Variation def

Answer 30

• expresses how much dispersion exists relative to the mean
• used in investment analysis to compare relative risk
• lower value is less risky

Question 31

Coefficient of Variation formula

Answer 31

= CV = S / ^x

• sample standard deviation / sample mean

Question 32

Properties of a Normal Distribution

Answer 32

• “symmetrical distribution”
• mean = median = mode
• completely described by the mean and variance
• skewness = 0
• Kurtosis = 3 (excess kurtosis = 0)

Question 33

Properties of a Positively skewed distribution

Answer 33

• has a long tail on the right side, peak to the left
• limited but frequent downside returns and unlimited but less frequent upside returns
• ie buying calls
• mean > median > mode
• positive skewness (>0)
• visually, the Mode is at the peak, the median is to its right and down the slope, the mean is further down the slope to the right

Question 34

Properties of a Negatively skewed distribution

Answer 34

• has a long tail on the left side, peak to the right
• limited but frequent upside returns and unlimited but less frequent downside returns
• ie selling puts
• mean < median < mode
• negative skewness (<0)
• visually, the Mode is at the peak, the median is to its left and down the slope, the mean is further down the slope to the left

Question 35

List the different Kurtosis’

Answer 35

• Leptokurtic
• Platykurtic
• Mesokurtic

Question 36

Properties of Leptokurtic

Answer 36

• fatter tails
• more peaked
• excess kurtosis > 0
• k > 3
• probability of loss is higher
• visually, the peak is higher and the tails come down steeper and go out further. thus there is more data in the tails (fatter)

Question 37

Properties of Platykurtic

Answer 37

• thinner tails
• less peaked
• excess kurtosis < 0
• K < 3
• visually the peak is lower

Question 38

Properties of Mesokurtic

Answer 38

• identical to a normal distribution

- K = 3

Question 39

Covariance def

Answer 39

• a measure of how to variables move together
• if positive, the 2 variables move up/down together
• if negative, the 2 variables move in opposite directions

Question 40

Sample Covariance formula

Answer 40

= Cov = sum of (xi - ^x)*(yi - ^y) / n - 1

Question 41

Correlation def

Answer 41

• a standardized measure of the linear relationship between to variables with values ranging between -1 and +1
• ie the strength of the relationship

Question 42

Sample Correlation formula

Answer 42

= cov / sx * sy

cov of xy / sample stdv of x * sample stdv of y

Question 43

Spurious correlation

Answer 43

• the correlation between town variables arising from their relation to a third variable.
• ie shoe size and vocabulary of school children
• the third variable is age