文档介绍：Investment Tools – Statistics
SASF CFA Quant. Review
1
Statistical Concepts
Population is defined as all members of a specified group.
Sample is a subset of a defined population.
Frequency Distribution: is a tabular display of data summarized into a relatively small number of intervals.
Frequency distribution is the list of intervals together with the corresponding measures of frequency for the variable of interest.
A histogram - graphical equivalent of a frequency distribution; it is a bar chart where continuous data on a random variable’s observations have been grouped into intervals.
A frequency polygon is the line graph equivalent of a frequency distribution; it is a line graph that joins the frequency for each interval, plotted at the midpoint of that interval.
2
Frequency Distribution Table
Raw Data:
24, 26, 24, 21, 27, 27, 30, 41, 32, 38
Class
Frequency
15 but < 25
3
25 but < 35
5
35 but < 45
2
3
Frequency Dist’n Table Steps
1. Determine Range
2. Select Number of Classes
Usually Between 5 & 15 Inclusive
3. Compute Class Intervals (Width)
4. Determine Class Boundaries (Limits)
5. Compute Class Midpoints
6. Count Observations & Assign to Classes
4
0
1
2
3
4
5
Histogram
Frequency
Relative Frequency
Percent
0 15 25 35 45 55
Lower Boundary
Bars Touch
Class
Freq.
15 but < 25
3
25 but < 35
5
35 but < 45
2
Count
5
0
1
2
3
4
5
Frequency Polygon
Midpoint
Fictitious Class
0 10 20 30 40 50 60
Class
Freq.
15 but < 25
3
25 but < 35
5
35 but < 45
2
Frequency
Relative Frequency
Percent
Count
6
Numerical Data Properties
Central Tendency (Location)
Variation (Dispersion)
Shape
7
Measures of Central Tendency summarize the location on which the data are centered.
Population Mean: calculated as
where there are N members in the population and each observation is Xi i =1, 2, …N.
Sample Mean: calculated as
where there are n observations in the sample and each observation is Xi i =1, 2, …n. It is also the arit