Stats

Section 2.1 Frequency Distributions and their Graphs

A frequency distribution is a table that shows classes or intervals of data entries with a count of the number of entries in each class. The frequency, f, of a class is the number of data entries in the class.


Example:

Classes Frequency, f

1-5 5

6-10 8

11-15 6

16-20 8

21-15 5

26-30 4

The left column shows the

organization of the data

entries into classes.

The right column shows the

frequency, i.e., the number

of data entries that fall into

that class.
————

Why do we use Frequency Distributions?

  • They can illuminate patterns about the data that are otherwise not obvious.

  • They allow us to quickly make observations about the data we’ve collected.

  • They set us up to do some basic mathematical analysis on our data. (We will see more of this later in the chapter.)

Lower class limit: The lower limit of a class is the least number that can belong to that class. That is, it is the lowest data entry that could be in that class.

Upper class limit: The upper limit of a class is the greatest number that can belong to that class—i.e., the largest data entry that could be in that class.



  • The frequency is the number of values within each group of your sample.
    MAKE SURE YOU COUNT THAT FIRST NUMBER WHEN MAKING your table based on class width. Then the number of rows is the number of classes/dividends

  • Relative frequency is a percent. Were gonna talk about it as decimals, although in the real world you should say a percent

  • Cumulaive frequency -

  • Midpoint = Lower class limit + upper class limit/2

  • lowercase n means sample size - How many r in your sample

  • Capital N is talking about population

  • Frequency histogram/histogram. - Graphically representations of the data distribution

    • The horizontal scale is quantatative, so all your class numbers

    • the vertical scale is your frequencies



Aug/31


  • Histogram practice

    • You can use midpoints or upper and lower limits


Graphing Qualitative Data

A Pareto chart is a kind of bar graph that allows us to display qualitative data. An important component of a Pareto chart is that they present the qualitative categories in order from highest frequency to lowest frequency.


Paired Data Sets

  • A paired data set consists of two data sets where each data entry in one of the data sets corresponds to a data entry in the other data set. Importantly, a paired data set relates two quantitative variables.

Example:

For instance, if a botanist is interested in studying the length and width of flower petals then they might use a paired data set. For every data entry in the petal length data set, will also have a data entry (corresponding to the same petal) in the petal width data set. Scatter Plots A scatter plot allows us to display paired data sets and illuminates the relationship between the two quantitative variables. Ch 2: Descr

9/9

Fractile Example: Quartiles

One commonly used example of fractiles are quartiles which arethree numbers that split an ordered data set into 4 equal parts.

  • First quartile Q1: The first quartile of a data set is the number that breaks the data into the least quarter and the greatest three quarters.

  • Second quartile Q2: The second quartile of a data set is the median of the data set.

  • Third quartile Q3: The third quartile of a data set is the number that breaks the data set into the greatest quarter and the least three-quarters.

STAR - Midterm question - Theres an essay question where you have to explain why we have quartiles, why their useful and why its different from standard deviation. Why cant we have outliers? WHy need both

9/18

Chapter 3

  • Probability is the measure of likelihood

  • Probability Ex

Key Vocab

  • Probability Experiment: A probability experiment is an action or trial through which specific results (counts, measurements, or responses) are obtained.

  • Outcome: An outcome is the result of a single trial in a probability experiment.

  • Sample Space: A sample space is the collection of all possible outcomes of a probability experiment.

  • Event: An event is a subset (part of) the sample space and it may consist of one or more outcomes.