Data Analysis Chapter 1

What is Statistics Statistics is a way for us to defend a side of an argument or a case supported by the collection of data using various tools and methods. Statistics is designed to help us better understand the world. A statistic is the actual mathematical calculation made from or collected from the data. Data – data are the numerical values collected in the context of a study or an experiment. DATA TABLES are very useful in organizing this information

The W’s of statistics The W’s of statistics provide us with the context of the study or experiment. Without the answer to the first 2 questions, the numbers are meaningless….like the number 99. Who – Did you collect the data on Respondents to a survey Subjects or participants in an experiment Experimental units such as animals, plants, or other inanimate objects What – the variable on which are collecting data When Where Why – tells us more about the reliability How – tells us about the validity of the collection method

Examples A consumer report magazine created a report on energy bars for the benefit of its readers. They provided the following data in the report: band name, flavor, price, # of calories, and grams of protein and fat. State each of the following: WHO: WHAT: WHEN: WHERE: WHY: HOW: WHY: CATEGORICAL VARIABLES: QUANTITATIVE VARIABLES:

3 RULES OF DATA ANALYSIS MAKE A PICTURE (helps you think about what patterns exists, and see deformities) MAKE A PICTURE (shows others what the important features of the data are) MAKE A PICTURE (best way to tell others your results)

2 Variables There are 2 major categories that collected data can be broken into Categorical Variables Examples: Quantitative Variables

Displaying/Describing Categorical data Bar Graphs (side by side bar graphs, segmented) Pie Charts Frequency Tables Two Way tables or Contingency Tables

Bar Graphs A Bar Graph is an easy way to display data side by side showing the counts of each category (largely different from histograms – which we will see later) There are small GAPS between the bars meaning these are freestanding bars and can be rearranged in any order. Therefore we cannot determine a pattern from a bar graph. There are various types of bar graphs as see below. Basic Bar Graph Side by Side Segmented

Pie Charts A pie chart takes 100% of the data and putting it into a circle my transforming the % into degrees and marking it off on the circle. Pie charts only work if you have all the data Pie charts give you a quick impression of the overall group

Frequency Tables Frequency tables are a way to organize the counts of your experiment into a table or chart that will allow you to better analyze the numbers. Counts are always helpful, but it is sometimes better to utilize the percentages or proportions to evaluate the data. A Relative Frequency Table shows the percentages rather than the counts of the data. Both are helpful in showing and describing the distrubutions across the varying categories.

Two Way Table Or Contingency Table A two way table shows the individuals distributed out over different variables. Each cell represents the number of individuals that are involved in both variables. There is a specialized type of two way table called a conditional which shows the distribution of 1 variable that is dependent on the other variable. (this will become very important in 2nd semester)

Examples The following table shows the number of seats in the US House of Representatives by Region following the 2000 Census: Create a Bar Graph and Pie Chart Location # of Seats Percentage Northwest 83 Midwest 100 South 154 West 98

Graphs

HOMEWORK

Displaying Quantitative Data There are various methods of displaying quantitative data to include: Dotplots Stem & Leaf Plots Histograms Relative Frequency Plots Cumulative Frequency Plots (Ogive) Box Plots

Vocab But before we learn about the different graphs….lets talk about so vocabulary Center – the middle number in a data set Mean, Median, Mode (in that order) Spread – Describes the distance across the data Standard Deviation, Range, IQR Shape – describes the overall design or look of the graphical organizer

Shape There are a large variety of terms used to describe the shape of a graph to include: Normal – which means it is spaced out like a bell curve Skewed right or left – means the data stretches to one side (the longer tail is the side of the skew) Symmetric Uniform – a histogram with no peak – same height everywhere Unimodal, Bimodal, multi-modal Gaps

Outliers An individual observation that falls outside the overall pattern There will be formulas later to perform mathematical calculations to determine precisely whether or not the data piece is an outlier.

Constructing a dotplot Created by labeling your x-axis with the #’s represented in the data, then placing a dot above it to represent each occurance on the graph.

# of Goals scored in Round 1 Example The number of goals scored by each team in the 1st round of the Olympic Soccer games is shown in the following table. Draw a dotplot, evaluate & describe the distribution. # of Goals scored in Round 1 4 2 0 1 3 1 2 6 3 0 1 0 3 1 2 4 3 0 1 0 2 1 1 0 5 3 1 0 2 0 0 0 1 4 2 1

Example Continued Center: Spread: Shape: Outliers: 0 1 2 3 4 5 6

Constructing a Stemplot Stemplots require 2 digit numbers that get split apart which stretches the distribution out You can however give data its second digit… 9 become 09

Example Type of Candy Fat (grams) Snickers Milky Way Kit Kat The number of grams of fat in a candy bar vary. The table below shows the amount of fat in each candy bar (made up values). Create a stem & leaf plot and describe the distribution. Type of Candy Fat (grams) Snickers Milky Way Kit Kat Butterfinger 3 Muskateers Heath Hershey Twix Almond Joy 16 19 14 22 24 9 11 31

Example Continued Stemplot Key Description: Center - Spread - Shape - Oulier -

HOMEWORK

HIstograms Histograms use bars much like the bar graph. The biggest difference is that there are no gaps between the bars in a histogram like there are in a bar graph. A histogram shows the distribution of the values where each bar represents a frequency of each bin. Bins are the width of each bar (set by you or your calculator) (we will address this as we get into problems) Bins can be set as individual numbers or ranges of numbers If a number lands on the line between the bins, you decide which side to put the number on (you must continue this way through the remainder of the problem)

Histogram Create a histogram for the following data and describe the distribution. Jan Feb Mar Apr May Jun July Aug Sept Oct Nov Dec 1997 -1.44 -.75 -.69 -.88 .12 .75 .81 -1.75 .69 -.22 -.16 .34 1998 .78 .62 2.44 -.28 2.22 -.50 2.06 -4.50 4.12 1.16 1999 3.28 3.34 -1.22 .47 5.62 -1.59 4.31 1.47 -.72 -.38 -3.25 .03 2000 5.72 21.06 4.50 4.56 -1.25 -1.19 -3.12 8.00 9.31 1.12 -3.19 -17.75 2001 14.38 -1.08 -10.11 -12.11 5.84 -9.37 -4.74 -2.69 -10.61 -5.85 -17.16 -11.59 By hand, start by creating bins, and make tally marks

Histogram

Histograms On the Calculator: Press Stat (Edit) Type the values into List 1 Press 2nd y= or Stat Plot Turn Plot 1 On Select Histogram Set the window to match intervals (for our example – X: -20 to 25) Y: 0 to 25 Select the scale (bin width) Press Graph

Histogram Example Use the data below to create a frequency table, histogram, and then describe the distribution 15, 16, 5, 7, 20, 19, 8, 13, 6, 17, 6, 9, 19, 6, 14, 8, 20, 5, 18, 8, 13, 7, 18.

Continued

HOMEWORK