MAT 119 Terms

Rational numbers

Can be broken down; ratio of two integers expressed as fraction

Prime number

Numbers whose factors are 1 and itself

Composite number

Opposite of prime numbers; have other numbers as factors.

Is 1 a prime number?

No, because it only has itself as a factor

Getting the LCDs of prime numbers

Multiply them together

Statistics

The science of collecting, organizing, analyzing, summarizing, and presenting numerical information in order to draaw inference.

Population

Aggregate / collection / whole of all subjects a researcher wants to study

Sample

Representative of a whole

Observational study

The subject is observed in their natural habitat

You don’t do anything to alter factors, you merely observe and record.

Experimental design / study

A treatment is done onto the subject

There are difference in variables / factors

Statistic

A numerical characteristic of a sample

E.g.: sample average

X-bar (x̄)

A statistical symbol for the sample mean (average) of a set of data.

It represents the sum of all values divided by the number of observations.

It is widely used in analytics to represent the average rather than the total population

Parameter

A numerical characteristic of a population

Mu (μ)

Represents the population mean or expected value, serving as a parameter to describe the average of an entire dataset, rather than just a sample

Qualitative data

Data that cannot be counted or measured

It is usually descriptive

Quantitative data

Data that can be counted or basic arithmetic can be performed on it

Convenience sample

Sample taken without scientific method

The closest, most affordable, or readily available sample is taken

Systematic sample

The nth individual is selected until the desired number of individuals are taken

E.g.: 3rd of every sample only

N vs. n

N = population

n = sample

Stratified sample

The population is divided into groups or subgroups called strata.

Individuals are selected from each group to make up a sample.

Cluster sample

The groups naturally exist and the researcher selects a desired number from each group called clusters.

Simple random sample

individuals are randomly selected from the population (frame) to attain the desired sample size.

In this method, every individual has an equal chance to be selected.

Variable

Factors

Frequency

The count or number

The count of how often a specific value, event, or data point occurs in a dataset

Category or class

The rows in a table

Individual

The subject of the study

“p” sign

Population proportion

MEAN or Sampling distribution of Sample Proportions

It is always equals to the population proportion

^p = sample proportion from a random sample,

It represents the proportion of a specific characteristic in a sample,

It is the percentage in the problem converted to a decimal.

Empirical Rule

(95% ≈ mean ± 2 standard deviations)

Z-Score Formula

Sample proportion - mean / standard deviation

Z-Score Rule

A common rule of thumb is that z-scores beyond about ±2 are considered unusual, because only about 5% of observations in a normal distribution fall outside that range.

Classic probability formula

P(event) = total number of possible outcomes / number of favorable outcomes

Relative Frequency

Relative frequency = Count or category / total

When asked to do a relative frequency table, place it beside the variable and frquency columns

The total should add up to 1 (can be a little more or less)

Creating a Pie Chart

Circle = 360 degrees

Multiple the relative frequency by 360

Histogram vs. Bar Chart

Histograms overlap with each other, bar charts do not.

Measure of Central Tendency

Mean, median, mode

Five Number Summary

Minimum

First Quartile (Q1)

Second Quartile (Q2)

Third Quartile (Q3)

Maximum

Mode

The most frequent value that appears in the data set

There can be no mode or multiple modes in a data set

Median

The middle value of the data set when arranged in ascending order

To find the rank of the median, use the formula: n+1 / 2

If the mean & median are not the same, go with the median

Mean

The arithmetic average of the data set

Unless stated, always assume that you’re computing for a sample (not population)

Mean = sum of data set / total number

Minimum

Lowest number from data set

First Quartile (Q1)

0.25(n + 1) tells you the rank of the number in Q1

Second Quartile (Q2)

0.50(n + 1) tells you the rank of the number in Q1

Also known as the median

Third Quartile (Q3)

0.75(n + 1) tells you the rank of the number in Q1

Maximum

The greatest number in the data set when arranged in ascending order

Box Plot

Also known as box and whiskers plot because of how it is constructed

Range of a Dataset

Max - min

Measures the spread of the dataset

Finding Outliers via the Five Number Summary

Outliers are numbers that are at or below the lower fence or at and above the upper fence.

Interquartile Range = Q3 - Q1

Lower Fence = Q1 - (1.5)(IQR)

Upper Fence = Q3 + (1.5)(IQR)

Shift of Distribution of the Dataset

Skewed to the right → use the median

Symmetric / bell shaped / normall distributed

Skewed to the left → use the median

Sample Standard Deviation

Square root of sample variance; OR

Square root of (sum of individual data)

Measure of a typical distance from each of the data points to the mean

Using Standard Deviation to Find Outliers

A data point or value below x̄ ± s2

Example:

IQ Test: If an IQ test has a mean of 100 and a standard deviation (s) of 15, then 2s

is 30 (2 × 15). Therefore, 95% of the population has an IQ between 70 (100 -30) and 130 (100 + 30).

Simple Linear Regression Formula

Prediction (y) = (slope x future time) + starting line

Every straight line on a graph follows a simple rule:
y = mx + b

Finding the Slope

(new value- old value) / (new time- old time)

Finding the y-intercept

any value - (slope x the value’s time)

Sample Variance

s² = Σ(xi - x̄)² / (n - 1)

(individual data - sample mean)² divided by (sample - 1)

Range

Midrange

When To Choose IQR Over Standard Deviation

When there is a significant number that can skew the data set significantly, since SD relies on the mean while IQR uses percentiles (which includes median or Q2).

Measures of Spread

IQR

Standard Deviation

Explanatory Variable

Explanatory variables cause or influence changes

Manipulated or observed to explain changes in the outcome

Response Variable

The variable that is measured to assess the effect of the explanatory variable in a study. It is often the outcome of interest in an experiment. It reflects the changes that occur as a result of variations in the explanatory variable.

Variables of Interest

Tthe specific factors, characteristics, or attributes a researcher measures or manipulates to answer a research questioni n a study. They include both the explanatory and response variables.

(Algebra) Term

An individual part of an algebraic expression

Separated by addition (+) or subtraction (–) signs, and can consist of numbers, variables (letters), or the product of numbers and one or more variables

Coefficient

What the number is called when it is being multiplied by a variable (letter)

Mathematical model

Often formulas that describe relationships between variables in the real world