[MMW] M4 - Data Management

statistics

deals with numerical and categorical data

numerical

categorical

statistics deals with __ __and__ ____ data

numerical data

data representing counts or measurements

categorical data

data that can be classified

observation

any recording of information

collection

presentation

analysis

interpretation of data

4 statistical methods

descriptive statistics

using numerical and graphical tools to get a better understanding of the information contained in a set of data.

statistical inference

* Comprises those methods concerned with the analysis of a subset of data leading to predictions or inferences about the entire set of data
* *Infer the expected amount of rain for July next year based on the average precipitation data for July in the past 30 years*
* *Estimate the average depths of a lake from measures taken from a  set of random areas*

population

N

\
* Consists of the totality of the observations with which we are concerned 
* May be finite or infinite

sample

n

\
subset of population

for the inference from the sample to be valid, the sample must be representative of the population

simple random sample

* n observations is a sample that is chosen in such a way that every subset of n observations of the population has the sample probability of being selected

tables

* Summarizes raw data into an organized list or distribution of counts and may include sums and proportions

bar graphs

often used to compare quantities in different categories

pie graph

used to show the distribution of proportions of parts to a whole

line graph

show information that is connected in some way like changes through time

frequency distribution table

* Organization of raw data in table form, using **classes** and **frequencies**

\
* Each class is defined by its **class limits,** which are the smallest and highest data value that can be included in the class
* **Class boundaries**  are numbers used to separate the classes so that there are no gaps i the frequency distribution
* *There must be 5 to 20 classes that are* ***mutually exclusive and exhaustive***
* ***They must be continuous and of equal widths***

class limits

* Each class is defined by its **_____,** which are the smallest and highest data value that can be included in the class

\

class boundaries

**______** are numbers used to separate the classes so that there are no gaps i the frequency distribution

\
must be **mutually exclusive and exhaustive**

continuous and of equal widths

histogram

graph of **frequencies** against **class boundaries**

frequency polygon

line graph of **frequencies** against **class marks**

\
must be closed at the lowest and highest boundaries

ogive

line graph of **cumulative frequency** with the **upper boundaries**

**MEASURE OF CENTRAL TENDENCY**

* Gives a single value that acts as a ***representative*** or ***average*** of all the values the outcomes of your data set

central tendency

goal is to identify a *single value* that is the best representative of the entire set of data

mean

average

median

midpoint of the data set when arrangegd from smallest to largest

mode

most frequently occuring category or score

measures of dispersion

* Measures of the **average distance** of each observation from the center of the distribution
* Summarize and describe the extent to which scores in a distribution ***differ from each other***

Tells us ***how spread out*** the scores are

range

highest - lowest value

\
simplest but most unreliable measure of dispersion since it only uses 2 values

variance

measure of how much the data points in a dataset vary or deviate from the average or mean value.

\
average of squared differences between data point and mean

\
squared of std dev

standard deviation

sqrt of variance

\
measure of how spread out the data is, but is easier to interpret because it is expressed in the same units as the original data.

percentile

* Measure indicating the value below which is a given percentage of observations in a group of observations fall

**PROBABILITY EXPERIMENT**

* Chance process that leads to well-defined results called outcomes

**OUTCOME**

* Result of a single trial of a probability experiment

**SAMPLE SPACE**

* Set of all possible outcomes of a probability experiment

event

* Consists of a set of outcomes of a probability experiment

**EQUALLY LIKELY EVENTS**

* Events that have the same probability of occurring

**CLASSICAL PROBABILITY**

* Assumes that all outcomes in the sample space are equally likely to occur