quantite methodologies CO1 (P1)

quandingle methods ;3

Descriptive Statistics

Describes the characteristics and properties of anything that you can gather data from (Person, Place, Companies). Based on facts or meaningful information. Cannot draw conclusions about larger sets of data.

Inferential Statistics

Draws conclusions about a population based on the data gathered from samples with the use of DS techniques, concerned with methods of analyzing smaller groups of data that lead to predictions about larger sets of data. Gives generalization about the whole from analyzing a part of it.

Population

Totality of all observations in which the dataset is obtained

parameter

A variable describing the population

Sample

a portion of a population, said portion will include as much diverse data as possible which will represent the entire population.

statistic

A variable describing the sample

Variables

parameters being studied in statistics

Qualitative Variables

nonnumeric data like gender, civil status, and location.

Quantitative Variables

numerical data like force, weight, voltage.

Continuous Data

This type of data needs to be obtained using measuring tools, measurable quantities but not countable, infinite values but has a range.

Discrete Data

countable and measurable quantities, finite values and only whole numbers. This data can be counted or measured using counting tools

Independent Variable

A variable that can be altered to see an outcome

Dependent Variable

A variable that is observed after altering an independent variable

Controlled Variable

A variable kept constant to avoid any influenced outcomes

Extraneous Variable

An unexpected/unplanned variable but with minimal effects to the outcome

Nominal

Assign numerical data to categorical data. Using counting to analyze data falling into a category

Ordinal Data

Assign rank to levels of data. Range for the ranks of the variable is not constant

Interval

Assign a constant difference between numeric data, addition and subtraction is applicable. Zero does not mean “nothing”.

Ratio

Assign continuous range of data over a range and allow all arithmetic operations. Zero means nothing.

Sampling

process of taking portions from the population.

Probability Sampling

eliminates biases against certain events with no chance of being selected, listing all possibilities and taking a chance that they will be selected to be part of the sample.

Non-Probability Sampling

Increases bias for certain events with no chance of being selected, not including all of the population in the sample.

Simple Random Sampling

arranging the population to a certain rule. Elements are numbered and a sample is taken by various randomizing principles.

Systematic Sampling

sample will be taken by dividing the population into equal groups and getting the kth element in each group.

Stratified Sampling

grouping the population into strata, random sampling is performed for each stratum proportional to the size of each stratum based on the population.

strata

a sample with generally similar characteristics.

Cluster Sampling

done by identifying groups known as clusters, must be similar to each other with respect to parameters being examined.

cluster

a subpopulation with elements as diverse as possible

Convenience Sampling

based primarily on availability of respondents.

Quota Sampling

There is a desired number of samples. Respondents were taken as they volunteered themselves to become part of the experiment.

Purposive Sampling

The sample is obtained based on certain conditions.

Textual Form

presenting data via sentences and paragraphs in describing data

Tabular Form

presenting data with tables arranged by row and column for various parameters

Graphical Form

presenting data with pictures

Ungrouped Data

Data points are treated individually. These are raw, individual data points that are not organized into groups or classes.

Grouped Data

Data points are treated as grouped according to categories, this is raw data that is arranged into classes or intervals

Frequency Distribution Table

Showing each value or range of values their frequent appearance in a dataset, used in statistics for larger sets of data to ease the interpretation and also for graphs

Reason to use Frequency Distribution Table

This procedure is used to lessen work by treating the data by group.

Class Limits

smallest and largest values that fall into class intervals and taken with equal number of significant figures as the given data.

range

r = highest value - lowest value

class amount

k = 1 + 3.322log(n)

class width

cw = r/k

Class Boundaries (tree class limits)

precise expression of class interval, usually one significant digit more than the class limit.

Class Boundary formula

Upper limit of Class A + Lower limit of Class B / 2

Class Mark

midpoint of a class interval

Class Mark formula

cm = Lower Class Limit + Upper Class Limit / 2

Cumulative Frequency Distribution

derived from frequency distribution and can be also obtained by adding class frequencies.

Relative Frequency

percentage of total frequency with respect to the total population

rf formula

rf = f/∑f

Relative Frequency Distribution (%rf)

percentage of frequency’s proportion in each class to the total frequency

%rf formula

%rf = f/∑f x 100

Less than cumulative frequency (<cf)

distribution whose frequencies are lower the upper-class boundary they correspond to

obtaining “<cf”

adding the frequencies from top to bottom

Greater than cumulative frequency (>cf)

distribution whose frequencies are above the lower-class boundary they correspond to

obtaining “>cf“

adding the frequencies from bottom to top

Frequency Polygon

points are plotted using the midpoint and frequency

Histogram

points are plotted using the midpoint and frequency

Ogive

points are plotted using upper(>ogive)/lower(<ogive) class boundary and cumulative frequency.

Pareto Chart

graph used to represent frequency distribution for categorical data and frequencies are displayed by the heights of bars, arranged from highest to lowest.

Bar Chart

graph similar to histogram. The height of each rectangle represents the frequency of that category, applicable for categorical data (or nominal level).

Pie Chart (Circle Graph)

circle divided into portions representing relative frequencies (or percentage) of the data.

Scatter Plot

used to examine possible relationships between two numerical variables. Two variables are plotted in x-axis and y-axis.

Time Series Graph

represents data occurring over a specific period under observation. Shows trend or pattern on the increase or decrease over the period

Pictograph

appropriate pictures are arranged in a row (sometimes columns) presented quantities for comparison.

Measure of Central Tendency

Statistical values that describe the center or typical value of a dataset, also helps in summarizing entire sets of data with a single representative number. Calculated by adding the highest value and the lowest value then dividing by 2

The Mean

Most used parameter for describing ratio data

Arithmetic Mean

Only measure under central tendency where sum of deviations of each value from mean is zero, affected by abnormally large or small values. Calculated by sum of all values and divided by number of values.

Geometric Mean

Used in factors multiplied to another quantity

Geometric Mean formula

GM = sqrt(ab)

Trimmed Mean

Removing upper and lower values of the distributing and obtaining the arithmetic mean. Calculated by trimming a certain percent of both the largest and smallest set of values

Trimmed Mean formula

TM = ∑%x/%n

The Median

Midpoint of the values, as many values above as well as below it, unaffected by extremely large or small values, computed for ratio-level data, interval-level data, ordinal-level data, and open-ended frequency distribution if not in an open-ended class.

The Mode

Value of observation appearing most frequently, used to find most occuring/frequent value, Most unreliable compared to other measures, only measurement that is used for nominal data.

Bi-modal

When distribution has 2 modes

Tri-modal

If distribution has three modes

Multi-modal

The distribution has more than 3 modes

Measures of Position

Describes the relative standing of a value in a dataset, Indicates where a particular data point lies in relation to the rest of the data, Main measurements are Quartile (Q), Decile (D), Percentile (P) and standard score (z).

Quantiles (or Fractiles)

points taken at regular intervals from cumulative distribution

Quartiles

Division of dataset in 4 groups

Deciles

Division of dataset in 10 groups

Percentiles

Division of dataset in 100 groups

Measure of Variation (or Dispersion)

describes how spread out or dispersed the values are in a dataset. Tells how far the data points are from that center, measurements are range, standard deviation, variance, quartile deviation, interquartile range, and coefficient of variation.

Range

Difference between largest to smallest number in the set

Variance

Average of square deviations

Standard Deviation (SD)

given as positive square root of population/sample variance

Coefficient of Variation (CV)

Percentage of the ratio of standard deviation to the mean

Mean Absolute Deviation (MAD)

Average of unsigned deviations from mean

Quartile Deviation (QD)

Absolute measurements of dispersion

Interquartile Range (IQR)

Spread of the middle 50% of the data

Measure of Shape

Describe the distribution pattern of data, specifically the values are spread and whether the distribution is symmetric, skewed, or has peaks of certain sharpness.

Skewness

Degree of asymmetry of distribution about a mean, measurement of how data departs from symmetry, can be interpreted as symmetric, and positively or negatively skewed.

Kurtosis

Degree of peakedness exhibited by the distribution, computed as the fourth-degree moment from the mean.