Analyzing Data Week 1

Types of Graphs

Histogram Must be Quantitative Data (measurements) Make “bins”, no overlaps, no gaps. Sort data into the bins Graph how many in each bin. Note the width of the bins can affect the shape of the distribution

Histograms on the TI-83 STAT==>EDIT Enter the data in one of the lists 2ND Y= Select Plot1, Plot2 or Plot3 Select On Select Histogram Select the correct list ZOOM 9

Histogram on the TI-83 To adjust the bins WINDOW=> Adjust the Xmin and Xmax Xscl controls the bin width Adjust the Ymin, Ymin Hit GRAPH to display, NOT ZOOM 9

Histogram Use to display a distribution Good for large quantities of data It is a summary graph. You lose the original data Purpose: Show the distribution.

Dot Plot A Dot plot is a ‘short cut’ graph that works much like a histogram. Make bins. No overlaps. No gaps. Make a dot in the correct bin for each data point. Good for small data sets (less than 100) Good for making a quick informal analysis. Purpose: Show the distribution

Stem and Leaf Must be quantitative data. Set up bins as the stems. Mark the data with the leaves. Works well with small data sets (less than 100) Keeps the original data values as part of the graph. Purpose: Show the distribution

Describing a Distribution Center: Where is the graph centered up? Shape: What does the graph look like? Spread: Where are the areas of concentration? Outliers: Are there any exceptional points

Describing the Center of a Distribution “Where is the middle of the graph?” “Where is the ‘average’ data value?” “Is there a ‘middle range’ of values?”

Describing the Shape of a Distribution Uniform: “Are all of the bars about the same height?” Symmetric: “Would it match up if you folded it in half?” Skewed: “Does it have a long tail on one side?”

Describing the Spread of a Distribution Maximum value Minimum value Is the graph concentrated in one range or it is spread out? Are there gaps in the data? Are there clusters of data with gaps in between?

Describing Outliers in a Distribution “Are there any data points that do not fit with the rest of the graph?” “Are there any data points that are ‘way off’?” If a data point does not ‘jump’ at you as being ‘weird’ it is probably not an outlier

Lets talk about numbers Describing a distribution with numbers

Numeric Descriptions of Center Mean The average value Median: The middle value size wise

Numeric Description of Spread Range: Max value - Min value Q1: The 25% mark. The data point that is the median of the bottom half of the data Q3: The 75% mark. The data point that is the median of the top half of the data. IQR: Interquartile range, Q3 - Q1

Numeric Descriptions of Spread Standard Deviation : Approximately the distance off the mean of an average data point.

Numeric Descriptions of a Distributions Five number summary: Minimum Q1 Median Q3 Maximum Use the five number summary when the distribution is not symmetric. It is always a good description of a distribution.

Numeric Description of a Distribution When a distribution is roughly symmetric we can use: Mean Standard Deviation Mean and Standard Deviation are more powerful in further computations, but only are valid if the distribution is near symmetric

Box Plot Must be quantitative data Is a summary graph. Original data is lost. Good for show the spread of the distribution It is a graph of the 5 number summary. Narrow regions => concentrated data

Making a Box Plot on a TI Data in L1 STAT PLOT Select the Plot number Turn it on Select Box Plot Select the correct list ZOOM-9

Describing Outliers Test for an outlier Find the IQR = Q3 - Q1 Lower cutoff = Q *IQR Upper cutoff = Q *IQR Any data point that is less than the lower cutoff or bigger than the upper cutoff is officially an outlier.