08.27.26-09.11.26 content

Investigative questions

• Used to obtain data

• make sure to get multiple data values

3 things an investigative question must do

• identify the population

• state a parameter (population proportion or population mean)

• Use comparative words like difference, increase, decrease, more/less than

Population

the collection of all subjects

sample

a small section of the population

census

asks all individuals (think US census) & collects data

Unbiased estimater

refers to a sample as it should be randomized

Parameter

characteristic from a population

Statistic

characteristic from a sample

Observational unit

an individual in the data set - must be specific

Variable

Characteristic that can take on different values from different observations

2 Types of variables

• categorical

• quantitative

2 types of quantitative variables

• discrete

• continuous

discrete variables

• takes on specific values

• measured by counting

• usually whole numbers

continuous variables

• can take on an infinite number of values in a particular range

• found by calculating

Categorical variables

• divided data into different groups

• usually not numerical

EX: your birthday, although a number, would fall under categorical because can’t do any measurements with the numbers unless its a question like “out of a sample of ___ people, what is the probability that ___ have a birthday in ___?” but even them I’m unsure

frequency table

categories and number of times occuring

relative frequency table

% of the total number of values

Bar graphs

• used to display categorical data

• the bars do not touch so they can be reordered

• x axis = categorical variable

• y axis = frequency or relative frequency

• scale equally and use proper scale - don’t lie with statistics!

• bars must also be equal width

Misleading graphs

• do not use pictographs!

• watch for bar size

• watch for scales

Dot plots

• used with discrete data

• smaller range data / small variability

• small data set in general

Different shapes (distributions & peaks)

Distributions

• Symmetric

• Skewed left (negatively)

• Skewed right (positively)

• Uniform

Peaks/Modes

• 1 = unimodal

• 2 = bimodal

• 3+ = multimodal

Graph unusual features

• Possible outliers

• gaps in the data

• clusters in the data

Measuring center: median vs mean

• use mean in uniform distribution = average of data

• Use median in anything skewed = middle value of data

Spread & variability

• Standard Deviation

• range = max-min

(Spread & variability) Inter Quartile Range

• AKA IQR

• Q3-Q1

Stem & leaf plots

• displaying more complex numerical data with larger variability / multiple digits

• Good for discrete data

• Stems can have multiple digits (on the left) (think of them like “bins”)

• the leafs are on the right (individual data values)

• Ideally, you want 5 stems or split your stems

Histograms

• measuring both discrete and continuous data

• Discrete - bin indication in the middle of bar

• Continuous - spaces between bins serve as bars

Mean as a measure of center

• μ = population mean (parameter - greek letter “mu”)

• x̄ = sample mean (statistic)

x̄ = (Σxi)/n

OR sum of all data values/number of data values

Σ pronounced as sigma

Median as a measure of center

• middle value of ordered data

• # values + 1 / 2 = observational number of the median

• if you get lets say 3.5, then the median is the average between the 3rd and 4th value in the data set

Greek alphabet for funsies