Sik Fan Lah - Statistics (1.1-1.5)

Statistics

a study of data

Data

• observations that have been measured, recorded, collected, analyzed, and reported for use

• contains info about a group of individual objects described by a set of data

• info is organized using variables

Sample

• a smaller group you actually collect data from

• the size of the sample is represented using the variable “n”

• Statistic

statistic

a value that describes a sample

Population

• the entire group you are interested in learning about

• the size of the population is presented using the variable “N”

• Parameter

parameter

a value that describes a population, usually estimated from a statistic

Datum

a single piece of info or one value collected from an observational unit

• example: 92 - one student’s test score

Data

a collection of data values (the plural of datum)

• example: 92, 85, 78, 90 - all student’s test scores

• Correct oh mango - “The data show a strong linear relationship.”

Observational unit

an item or individual from which a datum is collected

• example: The test scores from AP Stat Unit 1 Test from last year are observed

• Observational unit: Each student

• Datum: Single test score

An investigative question should…

• have a clearly defined purpose

• be decided before collecting data

• NOT change based on the results

A strong investigative question typically…

• identify the population

• identify the variable being measured

• is clear/measurable

• can be answered with data

Good investigative question :)

“What is the average number of hours of sleep per night for the 12th grade students at North High School?”

• identifies population and variable

• clear and measurable

Bad investigative question ☹

“Do teens sleep enough?”

• vague

• no measurable variable

Categorial Variable

• data that places individuals into specific groups

• sometimes called “qualitative” variables

• examples:

  • gender

  • colors

  • size (small, med, large, XL)

  • grades (A, B, C, F)

  • political party

Quantitative Variables

• data that takes on numerical values, where performing arithmetic operations makes sense

• sometimes called “numerical” variables

• these can be broken down into two types:

  • discrete

  • continuous

Discrete variables

• this is numerical data where whole numbers make sense to describe the data

• think of variables that you would count, and decimals don’t make sense to describe them

• examples:

  • number of siblings

  • number of pets

  • systolic blood pressure

Continuous variables

• this is numerical data where decimals would make sense to describe the data

• think of variables where measuring makes sense and a certain number of decimal places or intervals are used to report the values

• examples:

  • height

  • weight

  • time

Frequency Table

• frequency table is a way to display how many individuals fall into each category of a categorial variable \

• Frequency is also referred to as count

One-way frequency

the number of times each category is shown in the raw data

Relative frequency table

a table (or relative counts) that displays the percentage in each category instead

• to find the relative frequency:

  • you take the frequency in each category and divide it by the total

  • the resulting decimal is written as a percentage

percentages, relative frequencies, and ratios

all express the same idea

• all describe a proportion of the whole

Percentage

a proportion expressed out of 100

Relative frequency

a proportion expressed as a decimal or fraction

Ratio

compares the number in one category to the total number of individuals

Bar graph

• used to visually show the distribution of data

• Distribution is a term used to describe the visual display of data that shows the variable and how often the data takes each value

• to create a bar graph that displays data from a one-way frequency table or a relative frequency table:

  • make sure the bars DO NOT TOUCH

  • the order of the categories does not matter

Pie graph

• the total quantity (100%) is represented in the graph

• each wedge of the circle represents a component part of the whole

• ALWAYS PERCENTS

• to construct a pie graph:

  • start with a frequency table of the data and find the total count

  • find the relative frequency of each of the categories

  • take the relative frequency and multiply it by 360° to find the number of degrees the wedge will take of the circle (ARC MEASURE!)

Histogram

• the bars WILL touch, to communicate that this is quantitative data

• the x-axis must go in order from least to greatest

• the x-axis will be labeled with values between the bars

  • these values communicate what values are included in the bar, up to BUT not including, the upper boundary

Stemplots

• stemplots - sometimes called a stem and leaf plot

• they are similar to a histogram BUT the individual data values are still able to be seen

• an example - the ages of random selection of teachers in the building

• “stem” is to the LEFT of the line and represents the age digit in the tens place

• “leaf” is to the RIGHT of the line and represents the age digit in the ones place

  • Notes:

    • stem can be one digit or multiple digits

    • leaves are lined up by their stem and go in order from smallest to largest

    • REPEAT values are LISTED

    • between each stem, the leaves are aligned together

Back-to-Back Stemplots

• back-to-back steplot - separate the quantitative data into two categories

• stem will go in the MIDDLE of the graph, with each set of leaves branching out

  • data should still go in order from SMALLEST to LARGEST, with smaller leaves BEING CLOSER to the STEM

Split Stemplot

• split stemplot helpful if you have a lot of values in a single stem

• if you have many values, it can be helpful to “split the stem” to be able to visualize the data better

• first stem digit is for the leaf digits 0 to 4

  • second stem digit is for the leaf digits 5 to 9

Dotplot

• a simple type of graph that involves plotting the data values, with dots, above the corresponding values on a number line

• to construct dotplot:

  • draw a horizontal line and label your zxis with the name of your variable

  • scale the axis based on the values of the variable

  • mark a dot above the number on the horizontal axis corresponding to each data value

Choose the right graph - Histogram

Works best with:

• continuous and discrete data

• large data sets or data with a large range

Best features:

• shows the shape of a distribution very well

Examples:

• heights of students

• daily temperatures

• annual rainfall amounts

Choose the right graph - Stemplots

Works best with:

• discrete data

• medium range of values you do not want too many or too few stems

Best features:

• shows the shape of distribution while maintaining the original data values

Examples:

• test scores

• weights

Choose the right graph - Dotplots

Works best with:

• discrete data

• small range of values

Best features:

• emphasizes individual data values

Examples:

• number of books read

• number of goals scored