Probability and Statistics 12/11/2015

Statistics Review/ Excel: Objectives Be able to find the mean, median, mode and standard deviation for a set of data. Be able to make a Histogram for a set of data. Be able to analyze probability distributions and determine if they are Normal. Be able to use the tools in Excel to analyze larger sets of data.

Review: In your notebook Calculate the mean, median, mode and standard deviation for the following set of data –10, 12, 14, 9, 11 Create a histogram for the same set of data using the following class intervals. –9-10, 11-12, 13-14

A distribution of all possible values of a variable with an indication of the likelihood that each will occur –A probability distribution can be represented by a probability density function Normal Distribution – most commonly used probability distribution Probability Distribution Notes Definition Sketch of Distribution

“Is the data distribution normal?” Translation: Is the histogram/dot plot bell- shaped? Normal Distribution Distribution 1.Does the greatest frequency of the data values occur at about the mean value? (Mode = mean) 2.Does the curve decrease on both sides away from the mean? 3.Is the curve symmetric about the mean? Summarize in Notes

Frequency Data Elements Bell shaped curve Normal Distribution Distribution

Frequency Data Elements Mean Value Normal Distribution Distribution Does the greatest frequency of the data values occur at about the mean value?

Frequency Data Elements Mean Value Normal Distribution Distribution Does the curve decrease on both sides away from the mean?

Frequency Data Elements Mean Value Normal Distribution Distribution Is the curve symmetric about the mean?

What if the data is not symmetric? Histogram Interpretation: Skewed (Non-Normal) Right

What if the data is not symmetric? A normal distribution is a reasonable assumption.

Back to Excel… Functions Use functions to find the following statistics for the set of height measurements –Mean –Mode: –Standard Deviation (population) –Minimum –Median –Maximum Use your notes to find the formulas. Open the Excel document with the heights from last class.

Loading the Analysis Toolpak File -> Options Click Add-Ins -> Manage box -> Excel Add-ins Go Add-Ins available box, Select the Analysis ToolPak check box ->OK

Frequency Chart and Histogram Frequency Chart –indicates the frequency of occurrence within a class interval Histogram –graphical representation of the Frequency Chart

Frequency Chart and Histogram Select class intervals –Use ft intervals for height data –Define Bin values Bins give the boundary point between class intervals Values less than or equal to bin value (but greater than previous bin value) are counted 1) Create the Bin chart for the decimal height measures.

Frequency Chart and Histogram Select the Data Analysis Tool –Data tab > Analysis panel

Frequency Chart and Histogram Select the Data Analysis Tool –Data tab > Analysis panel –Choose Histogram tool –OK

Frequency Chart and Histogram x Select the Data Analysis Tool –Data tab > Analysis panel –Choose Histogram tool –OK –Select Input Range –Select Bin Range –Choose Output Range Select a cell on the worksheet –Select ‘Chart Output’ –OK

Selecting Input Range 1) Click on 2) Click and Drag to Select the Values to Graph 3) Hit ‘Enter’

Selecting Bin Range 1) Click on 2) Click and Drag to Select the Bin Values 3) Hit ‘Enter’

Chart Output 1) Click on ‘Output Range’ Button 2) Click to check ‘Chart Output’ 3) Click on a Cell on the Worksheet to select where the Histogram will show up. 4) Click ‘OK’

Frequency Chart and Histogram Frequency Chart Histogram

Correct Data Labels 2) Double click on ‘Bin’ to ‘Height’ 1) Double click on ‘Histogram’ and change to ‘Heights of Students’ 3) Double click on ‘Frequency’ and delete it.

Excel Worksheet Using the data from the Cube Measures Find the Mean, Median, Mode, Standard Deviation and create a histogram of the data. Push: Experiment with the Histogram, display other statistics on the data. YourNameCubeStatistics And complete the 3.3 Worksheet