STATS test 1

two branches of statistics

descriptive and inferential

define population

the set of all subjects/things/elements of interest to the study

define sample

a subset, or part, of a population which the data is actually obtained

• used to make inferences

define statistic

a description about a sample

define parameter

a description about the population

• usually unknown/estimated

four levels of measurement

Nominal

yes/no

• put data into categories without any order

Ordinal

low/middle/high

• can be qualitative or quantitative

Interval

involves numerical data with equal intervals between values but no true zero point

• subtract data entries

ex. temperature measurements

Ratio

a numerical value with equal intervals and no negativity

ex. $75,025 / $ 150,000 (exactly double)

Types of Data Collection

1. Observational Study

2. Experiment

3. Stimulation

4. Survey

Convenience Sampling

easy to obtain, not reliable though

Simple Random Sampling

every sample has an equal chance of selection

Stratified Random Sampling

the population id divided into subgroups and random samples are taken from those groups

Cluster Random Sampling

mini populations

Systematic Random Sampling

ex. selecting every 100th household and start randomly

The difference between Stratified and Cluster

Frequency Distribution

a table that shows classes of data entries with a count of the number of entries in each class

class width

the distance between lower or upper limits of consecutive classes

cumulative frequency

the sum of the frequencies of that class and all previous classes

• is equal to the sample size (n)

relative frequency

the portion, or percentage, of the data that falls in that class

• formula: class frequency/sample size OR f/n

class midpoint

the middle of each class

• formula: (lwr class lim) - (uppr class lim) / 2

• for every class set / can use it for any class

Ogive

a cumulative frequency graph / a line graph that displays the cumulative frequency of each class at its upper class boundary

stem and leaf plot

finding the mean

x̄ = ∑x / n (finding the mean of the sample)

μ = ∑x / n (finding the mean of the population)

When do we use the mean?

• taking every single data value into account

  • requires consistency, outliers have an affect

When do we use the median?

• often preferred when the data contains outliers (data is skewed)

When do we use the mode?

• nominal

• not used much

• categorical

weighted mean

different data values that have varying weights

• ex. syllabus hw/tests percentage weights

Data that has been “binned” into groups/classes/intervals

• uses the midpoint to estimate

mean = ∑frequency x midpoint / ∑ frequency