Chapter 10stud

Chapter 10/ Chapter 11: 

Chapter 10/ Chapter 11

Types of variables: 

Types of variables Categorical – Examples: Quantitative – Examples:

A good graph…: 

A good graph… We expect a good graph to show us the _________ of a variable ___________ tell us what values a variable takes on, and how often it takes them

What we expect from good graphs:: 

What we expect from good graphs: Everything is properly labeled. In particular, variables graphed are labeled and data source is listed ___________________________________ ___________________________________ ____________________________________ _____________________________________ Pay attention to what the eye sees. Be careful when selecting your scale and avoid visual distortions. - Will making a simple change make the graph better?

Examples of Bad Graphs: 

Examples of Bad Graphs Evaluate the following graphs and identify the problems

Slide10: 

Interpretation of the misleading pictogram

Representing the Data: 

Representing the Data When evaluating a graph look for _______, _______, ________,& _________ Look for the simple shape that describes the graph, if there is one Give the center and ____________ __________ – the lowest and highest numbers on a graph on the x-axis (usually excluding outliers) Look for striking deviations from that pattern An ____________ is any individual observation that falls outside the overall pattern of the graph

Shape, continued: 

Shape, continued A distribution can take on three distinct shapes: __________: the right and left sides of the graph are approximately mirror images of each other _________: the right side (the one with larger values) extends farther than the left side Think: ______________________ _________: the left side (the one with lower values) extends farther than the right side Think: ___________________ Evaluate the following for shape:

Main Tools: 

Main Tools Pie charts Bar Charts Line graphs Histograms Stem & Leaf plots

Pie Charts (who brought their protractor?): 

Pie Charts (who brought their protractor?) Use when you have one _________________ and one _________________________ variable Shows parts as _______________________ Less frequently used because it is difficult to see relative size of pieces and difficult to draw by hand To Draw: __________ _________________________________________ _________________________________________

Bar Charts: 

Bar Charts Use when you have one ______________ and one _________________ variable From this graph, we can easily see the distribution of the variable Distribution may not make sense when categorical variable doesn’t take on ordinal values (i.e. type of car) Label the title, x & y axes How to draw: Label X & Y axes Draw in bars To distinguish that we are graphing a categorical variable, _______________________________________________

Beware the pictogram: 

Beware the pictogram Our eyes react to the area and perceived volume of an image as well as height When all have same width and depth, volume and area vary in proportion and our eyes perceive the right impression Some graphs are a bit dull, so we may be tempted to replace with pictures, but beware! LESSON: _____________________________________ _____________________________________

Some data:: 

Some data:

Pie Chart: 

Pie Chart

Bar Chart (can we describe the distribution?): 

Bar Chart (can we describe the distribution?)

Bar Chart (how about now?): 

Bar Chart (how about now?)

Why not?: 

Why not? In the above two examples, there was no logical order to the data, so the shape could change based on whim Only in cases where the data has some definite order does it make sense to describe shape i.e. “How frequently do you bathe?” Daily or more often Every other day At least once a week Less than once a week

Line Graphs: 

Line Graphs Used for graphing quantitative variables that vary with time ex. Stock levels, water levels, average enrollment, etc. Line graphs allow us to look for Overall patterns or trends in the data Striking deviations from noted trends Patterns that repeat themselves over regular intervals of time, known as seasonal variations i.e. toy sales, gasoline sales When a series of measurements over time has been adjusted for seasonal variation, we call it seasonally adjusted. That is, the expected seasonal variation has been removed before publishing

Line graphs, again…: 

Line graphs, again… __________ is exceptionally important in line graphs, different _________ of the same data can lead to drastically different graphs (see figure 10.8, page 190) How to draw: Label time on the x-axis (watch scale) Label y-axis appropriate to data _______________________________ _______________________________

Histograms: 

Histograms Use when you have two _____________ variables Unlike a bar graph, there is no space between bars How to Draw: _____________________________________ _____________________________________ count the individuals in each group Graph the counts. You can also just graph how many times you observed each value (if the values happen often enough)

Stem & leaf plots (stemplots): 

Stem & leaf plots (stemplots) Use when you have two quantitative variables Only for small data sets For small data sets, stemplots are quicker and give more info. than a histogram How to draw Separate observations into stems, consisting of all but the rightmost digit and a leaf, the final digit. Stems may have as many digits as needed Write the stems in a vertical column with the smallest at top, draw a vertical line to the right of this column Write each leaf in the row to the right of its stem in increasing order out from the stem

Stem and Leaf Ex.: 

Stem and Leaf Ex. Make a stem and leaf plot from the following data 100,110,114,115,115,112,116,118,120 112,113,117,101,121

Stem plot: 

Stem plot 10 | 01 10 | 11 | 02234 11 | 55678 12 | 01 - here, each number has two stems, one for leaves 0-4, and one for leaves 5-9, the data will decide if you do it this way

Stem and Leaf -> Histogram: 

Stem and Leaf -> Histogram Data: 9.139390 10.006332 10.914331 10.208822 10.338834 10.270303 8.598192 11.228500 11.125305 8.792200 11.129662 9.480403 8.671006 8.363045 11.190484 10.170216 8.831375 9.636160 7.768600 10.077166 11.216280 10.710828 10.106226 9.932447 10.571347 11.503371 10.570241 9.574569 10.716896 9.045883 9.724697 10.752858 9.656393 9.858804 11.275125 9.670575 11.821458 11.503307 10.310123 9.882425 9.510283 9.890210 11.424119 12.021432 9.723942 9.217562 10.164064 10.591992 8.615614 8.837070 9.878755 10.932301 10.481524 10.413753 10.383784 9.670062 11.830865 10.776634 12.023399 9.752647 10.384052 10.100040 8.671583 9.484726 12.452465 10.882897 9.166928 10.463923 9.968243 8.067442 7.860014 10.455950 11.396175 11.684914 11.632299

Exercise:: 

Exercise: Create a histogram: Shoe sizes: (20) 9 9 10 10 6 10 10 13 8 10 9 9 7 9 9 8 11 9 9 10 Describe its shape, spread, center

Recap: 

Recap A good way to display data is using a graph When constructing a graph use good techniques When evaluating a graph/distribution look for patterns, outliers, variation, skewness etc. Try to describe distributions by the shape & center