Descriptive Statistics: Data & Measures

• Descriptive Statistics 1 covers key concepts, including statistical data and measures
• Version 1 of the material was released in July 2009

Week One

• Statistics involves scientific methods for collection, organization, summarization, presentation, and analysis of data
• Key goal is to draw valid conclusions based on this data analysis
• Statistics is a tool applicable in natural, applied, social sciences, and any field with numerical data
• Statistics includes data collection, computation, comparison, analysis, and interpretation
• Numbers from statistics are referred to as data
• Statistical analysis helps make decisions in the face of uncertainties in business and industry
• Statistical analysis helps prepare for market/product research, feasibility studies, and economic forecasting
• Statistical analysis is applied to crop yield analysis, animal diet optimization, and medicine advancements
• Statistical metrology aids astronomy, chemistry, geology, meteorology, and oil explorations
• Governments collect vast continuous data for decision-making related to expenditure, revenue, and population
• Government is the primary user and producer of statistical data
• Two main types of statistical data: primary and secondary
• Primary data provides first hand information on the topic
• Collection of primary data represents a difficult but important task for statisticians
• Investigator has greater confidence
• Investigator appreciates challenges because of direct involvement from data collection
• Primary survey reports are usually comprehensive and include term definitions
• Primary data advantages include researcher confidence, comprehensive reports, and clear definitions
• Primary data disadvantages include being time-consuming, expensive, and requiring manpower
• Primary data may also be obsolete by the publication time
• Secondary data is obtained from existing sources such as ministries, banks, and research institutions
• Secondary data sources are often collected as part of routine jobs
• Secondary data advantages include low cost, less time expenditure, and easy access
• Secondary data disadvantages include potential for misuse, restricted access due to protocol, and unknown precision
• Potential disadvantages with using secondary data; may not conform to needs, and may contain errors
• Statistics summarizes raw numerical data through measures like mean, standard deviation and coefficient of variation
• Statistical planning relies on historical data and enables one to plan for future
• Important for planning with analysis of historical data
• Quantitative random variables can be expressed numerically and are discrete or continuous
• Discrete variables assume fixed whole number values
• Continuous variables can take infinite values between two points and are often related to measuring devices
• Four types of data measurement: nominal, ordinal, interval, and ratio
• Nominal data uses numerals for labels and has no implied direction or properties
• Ordinal data ranks items for order of magnitude
• It does not show specific maginitude of the differences
• Interval data specifies observation/item magnitude and has equal intervals
• Arithmetic operations like addition/subtraction are possible
• Ratio data is the highest measurement scale with equality of order, intervals, and ratios, plus a knowledge of the true zero point

Week Two

• Bar charts are visual tools for comparisons among categories using bars of uniform width
• Bar charts are applicable only to discrete, categorical, nominal and ordinal data
• Bars in a bar chart should have appropriate dimensions and spacing
• Bar length corresponds to category frequencies, always with a label for clarity
• Multiple bar charts make comparisons of more than one variable
• Multiple bar charts can further consider other variables like age and sex
• Component bar charts can further consider other variables like age and sex

Week Three

• Pie charts uses sectors to represent relative magnitudes of data
• Arc length is proportional to its slice value
• Sector makes up a slice
• Pie charts display a part of a group with its whole
• Pie charts work best when the goal is to compare a category between 25% to 50% to the whole
• Pie charts work best when goal is single graph comparison not comparison between different pie charts
• Pie charts may become better by figure insertion or supporting tables are important to consider
• The pie chart will need to show the proportion of the whole by listing what each part is
• Provide a chart title with sex of study respondents as an example
• Calculation of degree share for each category with sex example shown

Week Four

• A histogram is a graph for frequency distribution that extends from a simple bar chart
• Histograms applies only to continuous data such as height and weight
• Bars have to touch in a histogram and unlike bars in a bar chart
• Area of bar relates directly to frequency of that class
• Rectangular bar is constructed to cover the intended class range
• Considerations for histogram creation is that you decide on interval classes

Week Five

• Central tendency measures how data clusters with typical distributions that values that individuals tend to cluster
• The measure describes the concentration in the middle
• Average refers to the center of set data by average mean median or mode
• Mean can be arithmetic, geometric, or harmonic
• Arithmetic mean is the primary focus
• Arithmetric mean involves ratio of the sum of data points in the data point series
• Arithmetic mean simply is the representative value that all elements obtain if the total were equal
• Mean can be found in ungrouped data where x is a read x Bar as an example
• In the coding statistical method, assumes a value within as the mean for the mean values
• For data point X1, X2...the mid point is (x) and its respective frequency is represented by f1, f2

Week Six

• In an array, the median is whatever value dives the data set into equal haves
• A median can follow the following procedures
• Arrange data from least to greatest
• label a group data point with x1, x2 ... xn
• if observation n is odd, use median formulas

Week Seven

• Quantiles split distributions into equal portions, including quartiles, deciles, and percentiles
• The three quartiles split data into four parts
• Nine deciles divide data into ten equal parts
• Ninety-nine percentiles divide the range into 100 even parts
• Quartiles are obtained with formulas or using the cumulative frequency curve
• Quartile calculation is similar between grouped and ungrouped data with respective modifications
• The equations follow L1 + (n/a-fc) / f1 * C as an example

Week Eight

• Dispersion measures the difference in size within a variable that indicates clustering around average
• Variance provides how well central tendency can represent particular distribution
• Some measures of dispersion is a range, simi inter quartile range, meand eviation variance and standard deviation
• Range R is a set of numbers as the largeset number to the smallest
• Quartile deviation is the sum as the difference between the third and first quadtile as explained in chapter 3
• Mean deviation = Σ/ x−x / , x = Σx/n = absolute value of the difference between x₁ and x N

Week Nine

• Statistical boxplots, also called box-and-whisker diagrams, show numerical summaries with 5 total entries
• Smallest sample minimum with first data and second quartile observations
• The plot aids what indicates observations that can be outliers
• Boxplot help show different poplulations without assumping underlying statistical data
• Help idenify data disperson and sketch
• Box plot is known with some conventions with drawing by creating set data horizontially
• A line on the numberline shows with Q1 ,median and and Q25
• Interquartile range calculated with first from the third
• Box lies with first the one listed and on its right
• The median must the box symbol

Week Ten

• Variance is related to standard deviation or standard average
• It is denoted by o²
• The sample variaince follows the equations Σ(x−x)² / n-1
• And standard deviation follows standard equation o²

Week Eleven

• Distribution are symmetric if capable of being cut with two symmetric image halves.
• Symmetric distributions yield bell shape curves
• Curve frequencies are always similar with equidistant from maximum
• Skew is asymmetry of distributions
• Asymmetric will have different tails relative on center
• For Skew presence: values will not coincide
• Freqencies arent similar at various positions
• Otherwise all must be satisfied symmetrical distribution
• Skewness calculates with Σ(x - X)³

Week Twelve

• Describes the q-q plot to access if 2 sets of data come from a common distribuation
• Is determined for 2 data sets to come from sample with a common distribution. q-q is fraction of values that has one percent
• Sample size is not always
• Axis axis is a estimated quantile

Week 13

• P-P Plot assesses the agreeance of two data sets, which charts 2 cumulative distribution functions to each set
• P-P Plot, a probability method to measure models with general or no comparable model
• By comparing if N numbers, can be given continous distribution that shows what is empirical
• The P p

Week Fourteen

• Probability sampling implies that every group in the population has a certain ability to be taken
• Probablity methods include random, startified, and clustering
• Selection procedure should have some random lottery or method without bias
• Stratiifed: divides set units internally to each sex type.
• Sympathtic: start random then keep the same order

Week Fifteen

• Data collection is intended to be both useful and insightful that data collections should be well chosen and have clear objectived
• Some methods of data collections include documentary, interview, questionnaire and observarion
• A questionnaire can help gather a certain objective and should allow some logical question/answer
• The survey can then sent to source
• It includes a general wide cost that is very timely
• Some disadvantage is ambiguous with no high cost given
• Interview method has the personal contact of the respondent
• Data collection needs careful planning to maximize effectiveness
• Data must be collected with respect to various objectives
• There are several advantages listed under the 15.2 heading
• Observation method includes certain systematic scientific methods to collect a lot of data that takes time Documentary records have the most time
• Documentary collects known info that has a lot of time and money cost given