Mode is another measure trying to capture the sense of majority
of the data. Intuitively, we typically think majority almost equals to
Definition. The mode the value in the data that occurs most
frequency Example 2.7. Q: What is the mo
2.2 Variation of the Data
In many cases, we care not only about the average/majority of
the data, but also care about how the data is distributed overall.
Example 2.10. Consider the household income of the two
following (island) towns, each with
Town 2: c
Example 2.5. Q: For data array A: cfw_zi = cfw_10, 14, 23, 28, 39, 90,
what is the median?
A: There is no single number that divides the data array into two
But 23,28 are in the middle position, so we use the average of
these two numbers, 23+28 =
2.1 Center of Data : Mean, Median and Mode
A most intuitive way to boil down information from data is to find
out about the average. For example, GPA condenses your grades
in many courses into one number to reflect your average
performance over all the cl
3.2.2 Putting the PDF to Work: Standard Normal Distribution
Definition. The standard normal distribution is the the normal
distribution with mean
= 0 and standard deviation = 1.
Mathematicians have calculated the areas below the standard
Normal density f
3 Chapter 6: Normal Probability Distribution
3.1 Primer3.1.1 Probability (Readings in Chapter 4)
Definition. The probability is the chance that a particular event will
occur. We denote the probability of outcome E by P (E).
For example, P (a dice turned o
Percentile is a gneralized concept from median. Median divides the
data array into two halves: it is the 50% cuto of the data array.
So, can we also have 20% cuto, 79% cuto, etc.?
Percentiles help us locate the position of a particular v
3.2 Normal Distribution (Gaussian Distribution)3.2.1
Probability Distribution Function (pdf) of Normal Distribution
The probability density function of the Normal distribution looks
like a bell, which is completely symmetrical and peaks in the
Population mean is a parameter, sample mean is a statistic.
Example 2.2. Q: Sample: 1,2,3,4; what is the mean?
Step 1 (determine sample size n): N = 4;
Step 2 (sum up the data): 1+2+3+4=10;
Step 3 (calculate the mean): x = ni=1 xi = 10 = 2.5 n4
3.1.3 Probability and Probability Distribution Function (pdf) of
Continuous Ran- dom Variable
This is the pdf for Normal distribution. The pdf takes a particular
form, which we will specify later. Because the Normal distribution
is most frequently identif