What is the definition of statistics?
What is the definition of statistics?
Description
School: Southern Methodist University
Department: Engineering
Course: Statistics for Business
Professor: Stephen robertson
Term: Spring 2016
Tags: Statistics, distribution, variables, chart, graph, stem plot, time plot, bar graph, histogram, mean, median, standard deviation, notation, and outliers
Cost: 25
Name: STAT
Description: Week 1 (through January 25) Includes: Examining distribution Variable types Distribution Chart/ Graph types Stem plot time plot measures of center &spread 5# summary Outliers Standard Deviation Notation
Uploaded: 02/02/2016
Reviews
Great notes!!! Thanks so much for doing this...
Chapter 1: Examining DistributionDon't forget about the age old question of What is the role of quantifiers?
Statistics - the science of data. The collection and analysis of data, often to make inferences about a population from a sample.
Population (all)We also discuss several other topics like ust notes
Sample If you want to learn more check out What is a separable ODEs?
Datasets contain information about “individuals”. Data organized into variables.We also discuss several other topics like What are the steps to develop economic model?
2 Types of Variables
1. Categorical Qualitative - individuals are organized into categories Don't forget about the age old question of What is another way at looking at the prices in the economy?
Ex: Male / Female, Fr/Soph/Jr/Sr, etc.
2. Qualitative - variables are measured in numerical values
(for which arithmetic operation make sense)
Ex. female: 0 ⎱ categoricalIf you want to learn more check out ucsc cmps 111
male: 1 ⎰
Exploratory Data Analysis - Beginning stage of statistical analysis
1. We examine the variables individually and in relation to each other
2. Use graphs and numerical summaries.
“Distribution” of a variable - a distribution that shows:
1) different values a variable can take on:
gender: 1) male 2) female
2) occurrences / # of times
result occurrences
Ex: flip a coin 10 times. What is the distribution of the (expected) result?
Result Occurrences
Head 5
Tales 5
Graphs for Categorical Variables: (Pie Charts and Bar Graphs)
1. Pie Chart
Time consuming by hand, so let excel do it!
Only works if you have all possible categories.
2. Bar Graphs
Easier to make than pie charts, and easier to read.
Graph for Quantitative Variables: (Histograms, Stemplots, and time plots)
1. Histogram - like a bar chart, except no gaps between bars (Because horizontal axis a # line)
Describing Distributions: Indicate the shape, center, and spread of a histogram, and “outliers”.
Ex:
Shape is normal
Center is 70
Spread is 40-100
Outliers? Unusual points
Grades on Exam
Skewed Distributions:
Skewed Right Skewed Left
Describing Distributions with Graphs
1.1 ex:
Stem plots grades in a class;
- Good for small sets (57, 59, 66, 67, 68, 74, 74, 76, 93)
(if you turn ideas;skewed “stem” 5 |7 9
to the right, most grades in 6 |6 7 8 “leaf”
60s and 70s, outlier is 98) 7 |4 4 6 ⤶
8 |
9 | 8
Time plots Ex: gas price per gallon
- Measures a value across time
(don't think about skewness)
Look for trends (patterns over the long term) and
cycles (patterns over short term) ← seasons, holidays, etc
1.2
Describing distribution with numbers
Measures of center
- Mean (average)
- Easily affected by outliers
- Median (middle)
- Large data sets
- Count up
observations from the bottom of the list.
- Ex: sample size of 16
Mean and Median can be different.
The median is resistant to outlier, unlike mean
(uses every valve will feel effect of outliers)
- normal - right skewed - left skewed
- mean = median - median < mean - median > mean
Measures of spread
- Quartiles (percentiles)
- (Q1) is the value where 25% is smaller
- (Q2) is the value where 50% is smaller
- (Q3) is the value where 75% is smaller
median → (Q2)
How to calculate (by hand) quartiles?
1. Order data set in ascending order
2. Find median
3. For Q1 find median below actual median
For Q3 find median above actual median
Ex:
1) (n=8) 1, 4, 10, 12, 16, 18, 28, 30 Find Q1 and Q3
Median = 14
Q1: 7
Q3: 23
