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SMU / Engineering / STAT 2301 / What is the definition of statistics?

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
6 Pages 219 Views 2 Unlocks
Reviews

Kaela (Rating: )

Great notes!!! Thanks so much for doing this...



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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

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