U1

Categorical data

Categorical data

refers to data that can be divided into categories or groups based on qualitative characteristics.

categorical variable

is one that represents characteristics or qualities rather than numerical values. It consists of categories or groups into which data can be classified.

center

refers to the middle or average value of a data set. It represents the typical or central value around which the data tends to cluster.

Descriptive statistics

involves organizing, summarizing, and presenting data in a meaningful way to describe its main features.

Inferential statistics

involves using sample data to make inferences or draw conclusions about a population.

Outliers

are extreme values that significantly differ from other values in a dataset. They can greatly affect statistical analyses and should be carefully examined.

Predictive modeling

involves using historical data and statistical algorithms to make predictions about future outcomes.

proportion

is a fraction or percentage that represents the relationship between a part and a whole in a population or sample.

• Categorical

  • groups

  • proportions to measure

  • eye color, statuses

    • visualized via __________

• bar graph, pie chart, table, mosaic plot

• Quantitative

  • measured, counted

  • means to measure

  • height, age

    • visualized via _____

• histogram, stem leaf, box whisker

• Five number summary

  • left to right on box plot: ______

• minimum, q1, median, q3, maximum

Quantitative data

refers to numerical information that can be measured or counted. It involves quantities and can be analyzed using mathematical methods.

SOCS to describe DISTRIBUTION

shape, outlier, center, spread

shape

symmetry skewness modality

outlier

strong variation from other values that affect stat measures; determine with 1.5IQR, 2SD rule

center

mean median mode

spread described by

range (IQR), variance, stand dev

IQR equals

q3-q1

standard deviation does

measures how far values are from mean

variance

measures variability

uniform

height approx same everywhere, no significant mode

• _ is easily affected by outliers, best measure of central tendency unless skewed / outliers

• __ is OUTLIER RESISTANT; better measure or central tendency when data skewed, outliersmean is easily affected by outliers, best measure of central tendency unless skewed / outlier

mean, median

z score is equal to

data point minus mean value all divided by standard deviation

• categorical: ____

• quantitative: _____

• bar graphs, NOT _____

• watch the scale!

• frequency = ____

• relative frequency =____

• qualitative, numerical, histograms, count, percentage

• describing distribution: SOCS (____________)

• ____ is affected by skew, ____ is not

• histograms: if comparing distributions w/ diff. sample sizes, use ______

shape outlier center spread, mean, median, relative frequency

• IQR = Q_-Q_

  • middle 50% of observations

• finding Q1,Q3:

  • odd: exclude _____ (Q2)

  • even: split ____

• five-number summary (1-Var Stats): ____

  • turn into box plot (use TRACE to find outliers)

• standard deviation: typical distance from ___

1,3, median, median, min, Q1, Q2, Q3, max, mean

describe how standard deviation is calculated

find the sum of initial x minus x raised to the negative second power. divide by

continuous data

numerical data that can take on any value within a given range. infinite possible values

interval level of measurement

is a type of measurement scale that not only categorizes data but also allows for meaningful comparisons between the values. It has equal intervals between the numbers, but there is no true zero point.

nominal level of measurement

is the lowest level of measurement where variables are categorized into distinct groups or categories based on their characteristics or attributes.

ordinal level of measurement

a type of measurement scale where variables are ranked or ordered based on their attributes. The order matters, but the differences between values may not be equal or meaningful.

ordinal variable

is a type of categorical variable that has a natural order or ranking. The categories can be ranked or ordered based on some characteristic or attribute.

contingency table is a type of table that is used to organize and (later on) analyze ____ data. It shows how the observations in a dataset are distributed among different _____ of two or more variables.

categorical, categories

ratio level of measurement

similar to interval level, as it allows for meaningful comparisons and equal intervals. However, ratio level also has a true zero point which represents an absence or complete lack of the measured attribute.