Isom 2500 - Cheat Sheet

ISOM 2500                                    1st Midterm Exam Revision Notes

Statistics Terms

1. Population：A group of all items of interest under study
2. Census: Survey that includes every member in the population
3. Parameter: A numerical descriptive measure of a population
4. Sample: A part of population
5. Statistic: A numerical descriptive measure of a sample
6. Variable: is some characteristic of a population or a sample
7. Data/Datum: Observed values of a variable
8. Observations/Case: The set of measurements obtained for a particular element
9. Elements: Entities on which data are collected

Types of Variables

1. Categorical/Qualitative variable: Non-numerical variables

1. Numerical/Quantitative variable: Numerical Data

1. Discrete Variables: Variables that are integers

1. Continuous Variables: Variables can be any real number

Nominal Data: Applies to data that are divided into different groups (E.g. Gender)

**Note that only calculations based on frequencies or % percentages of occurrence are valid

Ordinal Data: A type of nominal data where can be sorted or ranked.

**Note that the data may be treated as nominal but not as interval

Interval Data: Applies to data that can be sorted and for which the difference can be counted and interpreted, has an arbitrarily-defined zero.

**Note that an interval data can be treated as ordinal or nominal as well

Ratio Data: Applies to data that can be sorted and for which the difference and ratio can be calculated and interpreted, has non-arbitrarily defined zero.

Describing One Categorical Variable[pic 1][pic 2][pic 3][pic 4]

Tabular Display – Frequency distribution[pic 5]

Graphical Display: Pie chart, bar chart

Relative frequency of a category =   [pic 6]

Percent relative frequency of a category = [pic 7][pic 8]

Describing Two Categorical Variables

Tabular Display: Contingency Table Graphical Display: Cluster bar chart

Describing One numerical variable

Tabular Display: Frequency distribution // Summary table

Graphical display: Dotplot, Stem and Leaf diagram, histogram, polygon and Ogive 

The number of observations falling in each class is called the class frequency

Steps for constructing a frequency distribution for numerical variable:

1. Sort the data
2. Determine the range where range equals to the largest observation minus the smallest observation
3. Determine the number of classes k using Sturges’ formula: , where n is the sample size, round up the k.[pic 10][pic 9]
4. Divide the range by k to determine the class width[pic 11][pic 12]
5. Determine the class limits[pic 13]

Dotplot

A horizontal scale on which dots are placed to show the numerical values of the data points. If a value repeats, the dots will pile up at that location, one dot for one repetition.

**Note that the dotplot is only useful for small sample size where n is less than 30

Stem-and-Leaf Diagram

A partly tabular//graphical way of summarizing data and it is suitable for moderate to large data sets (usually less than 100 observations)[pic 14]

Histogram

A bar chart for numerical values whose areas are proportional to relative frequencies of respective classes, for the sample size greater than or equal to 30. Note that the shapes of histograms can be bell-shaped, positively-skewed or negatively-skewed.

[pic 15][pic 16][pic 17][pic 18][pic 19][pic 20]

[pic 21][pic 22][pic 23][pic 24][pic 25][pic 26][pic 27][pic 28]

Polygon