Data Analysis - ISEE 120

Population

• Total set of observations that can be made

• The set of data (numerical or otherwise) corresponding to the entire collection of units about which information is sought

Sample

• a set of observations drawn from a population

• A set of data collected and/or selected from a population by a defined procedure. 

• Necessary to use sample for research 

  • Impractical to study whole population

  • Rely on samples to make estimates related to population

Data

numerical facts

Statistics

• measurement and modeling of random variables

• estimates of population parameters

Continuous

values that can be measured (decimal/fractional)

Discrete

values that can be counted (whole numbers/distinct)

Graphical Data

used for quick information relay

Histograms

• visual representation of distribution of quantitative data

• x-axis = “bins”, y-axis = count of values

Line Charts

• uses points connected by line segments (left to right) to demonstrate changes in value

• X-axis = time, y-axis = reported values

• can also be used for comparison of data

Correlation Graphs (Scatter Plots)

• values represented as dots, showing a relationship between two variables, correlation shown by shape of the dots

• x-axis = factor 1, y-axis = factor 2

Pie Charts (% Charts)

• shows the total sum of a whole, and what percent each makes up

Pareto Chart

• similar to a bar chart, sorts values highest to lowest

Bar Chart

• compares two values with bars either stemming from the y or x axis, looks similar to Pareto charts or histograms

Mean

• the average of all values

Median

• the middle value in a chronological set of data

Mode

• the most frequent value in a data set

Range

• the difference of the largest and lowest values

Standard Deviation (SD)

• the square root of the variance

• used to measure distance away from mean to calculate certain percentiles

Normal Distribution

• SDs from mean in a normal bell curve

• 1SD ~ 68.26%, 2SD ~ 95.44%, 3SD ~ 99.73%

• S=sqrt((E(x₁-x₂)²)/(n-1)

Normal Bell Curve

• the common distribution of values in data sets

• resembles a bell

Variance

• the average squared distance each observation is from the mean

• S²=(E(x₁-x₂)²)/(n-1)

Standard Error (SE)

• variability across multiple samples of a population

• Quantifies uncertainty in the estimate of the mean

• As sample size increases, sampling error decreases

• SE=S/sqrt(n)

Confidence Interval (CI)

• a range of values we are fairly sure our true value exists in. 

• CI = X+/-Z(S/sqrt(n))

• 95% confidence interval marks the bounds within which 95% of the sample means will fall, given certain facts about the population and the sampling process. 

  • Lower Bound = u - 1.96*SE

  • Upper Bound = u + 1.96*SE

Z-Score

• +/- number of SDs a percentile is away from mean

• use z-score chart in this course