Data Science Training Courses Part 9

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Welcome to
Data Science Course in
Bangalore
DataMites Part 9
Accredited by IABAC™

Order of Operations
BRODMAS
DATA SCIENCE FOUNDATION 2
1. All calculations within parentheses are done first.
2. Squaring or raising to other exponents is done second.
3. Multiplying, and dividing are done third, and should be
completed in order from left to right.
4. Summation with the Σ notation is done next.
5. Any additional adding and subtracting is done last and
should be completed in order from left to right.

Methods used to collect data
Experiment: The investigator controls or modifies the environment and observes the effect on the
variable under study.
Survey: Data are obtained by sampling some of the population of interest. The investigator does
not modify the environment.
Census: A 100% survey. Every element of the population is listed. Seldom used: difficult and time-
consuming to compile, and expensive.
Judgment Samples: Samples that are selected on the basis of being “typical.”
Items are selected that are representative of the population. The validity of the results from a
judgment sample reflects the soundness of the collector’s judgment.
Probability Samples: Samples in which the elements to be selected are drawn on the basis of
probability. Each element in a population has a certain probability of being selected as part of the
sample.

Mean (μ)
The arithmetic average (add all of the scores together, then
divide by the number of scores)
μ = ∑x / n

Median
• The middle number (just like the median strip that divides
a highway down the middle; 50/50)
• Used when data is not normally distributed
• Often hear about the median price of housing

Mode
• The most frequently occurring number
(score, measurement, value, cost)
• On a frequency distribution, it’s the highest
point (like the á la mode on pie)

Standard Deviation (σ)

Mistakes while analyzing data
Alpha level
• Set BEFORE we collect data, run
statistics
• Defines how much of an error we
are willing to make to say we
made a difference
• If we’re wrong, it’s an alpha error
or Type 1 error
p value
• Calculated AFTER we gather the
data
• The calculated probability of a
mistake by saying it works
• AKA: level of significance
• Describes the percent of the
population/area under the curve
(in the tail) that is beyond our
statistic

Shape of Data
• Shape of data is measured by
– Skewness
– Kurtosis
Skewness
Measures asymmetry of data
Positive or right skewed: Longer right tail
Negative or left skewed: Longer left tail
2/3
1
2
1
3
21
)(
)(
Skewness
Then,ns.observatiobe,...,Let













n
i
i
n
i
i
n
xx
xxn
nxxx
Kurtosis
Measures peakedness of the distribution of
data. The kurtosis of normal distribution is 0.
3
)(
)(
Kurtosis
Then,ns.observatiobe,...,Let
2
1
2
1
4
21














n
i
i
n
i
i
n
xx
xxn
nxxx

Summary of data set
DATA SCIENCE FOUNDATION
1
Mean 90.41666667
Standard Error 3.902649518
Median 84
Mode 84
Standard Deviation 30.22979318
Sample Variance 913.8403955
Kurtosis -1.183899591
Skewness 0.389872725
Range 95
Minimum 48
Maximum 143
Sum 5425
Count 60
Histogram of Age
Age in Month
NumberofSubjects
40 60 80 100 120 140 160
0246810

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