CFAI - Formula - Org., Vis., and Desc. Data

Question 1

Data type: NOIR

Answer 1

Categorical

N - nominal. No logical order.

O - ordinal. Has logical order or rank.

Numerical

I - integer. Discrete > limited to a finite number of values.

R - ratio. Continuous > can take on any value within a range,

Question 2

Expected Value i,j

Answer 2

(Total Row i × Total Column j)/Overall Total

Question 3

Definition of Arithmetic Mean.

Answer 3

The arithmetic mean is the sum of the values
of the observations divided by the number of observations.

Question 4

Sample Mean Formula

Answer 4

Question 5

Definition of Median

Answer 5

The median is the value of the middle item of a set of items that has been sorted into ascending or descending order. In an odd-numbered sample of n items, the median is the value of the item that occupies the (n + 1)/2 position. In an even-numbered
sample, we define the median as the mean of the values of items occupying the n/2 and (n + 2)/2 positions (the two middle items).

Question 6

Mean. Even number of observations.

Answer 6

If a sample has an even number of observations, the median is the mean of the two
values in the middle. For example, if our sample in Exhibit 38 had 12 indexes instead
of 11, the median would be the mean of the values in the sorted array that occupy
the sixth and the seventh positions.

Question 7

Definition of Mode

Answer 7

The mode is the most frequently occurring value in a
distribution.

Question 8

Weighted Mean Formula. The weighted mean Xw (read “X-bar sub-w”), for a
set of observations X1, X2, …, Xn with corresponding weights of w1, w2, …, wn,
is computed as:

Answer 8

Question 9

Geometric Mean Formula. The geometric mean, XG , of a set of observations
X1, X2, …, Xn is:

Answer 9

Question 10

ln

Geometric Mean Formula. The geometric mean, XG , of a set of observations
X1, X2, …, Xn is:

Answer 10

Question 11

Alternative ln

Answer 11

Question 12

An equation that summarizes the calculation of the geometric mean return, RG

Answer 12

Question 13

Geometric Mean Return Formula. Given a time series of holding period
returns Rt, t = 1, 2, …, T, the geometric mean return over the time period
spanned by the returns R1 through RT is:

Answer 13

Question 14

Harmonic Mean Formula. The harmonic mean of a set of observations X1, X2,
…, Xn is:

Answer 14

Question 15

Deciding Which Central Tendency Measure to Use

Answer 15

Question 16

The formula for the position (or location) of a percentile in an array with n entries sorted in ascending order is:

Answer 16

Question 17

Quantiles

When the location, Ly, is a whole number

Answer 17

the location corresponds to an actual
observation. For example, if we are determining the third quartile (Q3) in a
sample of size n = 11, then Ly would be L75 = (11 + 1)(75/100) = 9, and the third
quartile would be P75 = X9, where Xi is defined as the value of the observation
in the ith (i = L75, so 9th), position of the data sorted in ascending order.

Question 18

Quantiles

When Ly is not a whole number or integer

Answer 18

Ly lies between the two closest integer numbers (one above and one below), and we use linear interpolation between those two places to determine Py. Interpolation means estimating an unknown value on the basis of two known values that surround it (i.e., lie above and below it); the term “linear” refers to a straight-line estimate.

Question 19

interquartile range

Answer 19

interquartile range is the difference between the lowest
value in the second quartile and the highest value in the third quartile

Question 20

Whisker plot

upper fence / lower fence

Answer 20

Upper fence: (1,5* IQR) + upper bound

Lower fence = lower bound - (1,5*IQR)

Question 21

Definition of Range. The range is the difference between the maximum and
minimum values in a dataset:

Answer 21

Range = Maximum value − Minimum value

Question 22

Mean Absolute Deviation Formula. The mean absolute deviation (MAD) for a
sample is:

Answer 22

Question 23

Here’s how to calculate the mean absolute deviation.

Answer 23

Step 1: Calculate the mean.

Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

Step 3: Add those deviations together.

Step 4: Divide the sum by the number of data points.

Question 24

Sample Variance Formula. The sample variance, s2, is:

Answer 24

Question 25

Sample Standard Deviation Formula. The sample standard deviation, s, is:

Answer 25

Question 26

Steps to Calculate Sample Standard Deviation and Variance

Answer 26

Question 27

Sample Target Semideviation Formula. The target semideviation, sTarget, is:

Answer 27

To calculate a sample target semideviation, we first specify
the target. After identifying observations below the target, we find the sum of the
squared negative deviations from the target, divide that sum by the total number of
observations in the sample minus 1, and, finally, take the square root.

Question 28

Calculating Target Downside Deviation

Answer 28

Question 29

Coefficient of Variation Formula. The coefficient of variation, CV, is the ratio
of the standard deviation of a set of observations to their mean value:

Answer 29

Higher = higher dispersion

Lower = lower dispersion

Question 30

Summarizing kurtosis:

Answer 30

Question 31

Relation aritmetic mean and geometric mean (MM)

Answer 31

s² = variance

Question 32

Skew

Answer 32

Skew = o

mean = median = mode

Skew > 0

mean > median > mode

Skew < 0

mean < median < mode

(tip: alphabetical order / arrows same direction)

Question 33

Excess kurtosis

Answer 33

alphabetical ordem

Question 34

Kurtosis summary CFAI

Answer 34

Question 35

Kurtosis summary MM

Answer 35

Question 36

Sign convention MAD

Answer 36

In calculating MAD, we ignore the signs of the deviations around the mean. For
example, if Xi = −11.0 and X = 4.5, the absolute value of the difference is |−11.0 − 4.5|
= |−15.5| = 15.5