1. EXCEL CHAPTER 6 ANALYZING DATA STATISTICALLY

2. Analyzing Data Statistically Data Characteristics Histograms Cumulative Distributions Classwork: 6.1, 6.6, 6.13 Homework: 6.4, 6.7, 6.11, 6.14

3. DATA CHARACTERISTICS Mean: AKA “average”. Measure of central tendency. Indicates expected behavior of a data set. Median: Measure of central tendency. Half of data lies above and half of data lies below the median. Mode: Measure of central tendency. Value that occurs most often. Data may have NO modes, 1 mode or more than 1 mode. Min: The minimum algebraic value in a data set. Max: The maximum algebraic value in a data set. Variance: Measure of spread in data. The greater the spread, the greater the variance. ADA “second moment about the mean”. Units are SQUARED. Standard Deviation: Measure of spread. Units are

4. STATISTICS FNS in EXCEL AVERAGE (C1:C12): mean of values in cells C1 to C12. MEDIAN (C1:C12): median of values in cells C1 to C12. MODE (C1:C12): mode of values in cells C1 to C12. MIN (C1:C12): minimum algebraic value in cells C1 to C12. MAX (C1:C12): maximum algebraic value in cells C1 to C12. VAR (C1:C12): variance of values in cells C1 to C12. STDEV (C1:C12): standard deviation of values in cells C1 to C12.

5. More Statistics in ExCel Make sure the Analysis Toolpack is installed. FILE-OPTIONS-ADDINS. If not there, then Manage: Excel Add-ins/Go and choose Analysis Toolpack and click on OK. To get a full statistical description from the DATA tab, choose DATA AYALYSIS from ANALYSIS Group and then select DESCRIPTIVE STATISTICS.

6. Classwork & Homework In the Classwork template, fill in the definitions of the various statistical fns. Do Prob. 6.1, using the template. Save as LastName_FirstName_CW6Excel Homework is Problem 6.4

7. Histograms Plot of RELATIVE FREQUENTY, how often data occurs within certain data ranges. AKA FREQUENCY PLOT. Once you have the Histogram, you can obtain the Cumulative Distribution which allows you to estimate the likelihood of an item drawn at random is less than or greater than some specified value.

8. PREPARE A HISTOGRAM Separate the data into a series of adjacent, equally spaced intervals (AKA bins). The first interval must begin at or below the MIN of the data set, and the last interval must end at or below the MAX of the data set. The intervals are AKA CLASS INTERVALS. Then determine HOW MANY data values fall within each interval. Note that you are NOT PLOTTING the actual data values, merely how many data values fall within a given interval. If the data value falls on an interval boundary, ASSIGN the value to the LOWER interval (consistent with Excel, not necessarily consistant with standard statistical practices).

9. PREPARE A HISTOGRAM- con’t Once you know how many data values are in each interval (bin) you can find the relative frequency by dividing the number of data values in an interval by the total number of data values. You get a decimal value less than 1. Notice that this corresponds to a percent.

10. Excel Histogram Generation It can be very tedious to determine how many data points are in each interval if you have more than 10 or 15 data points. Excel will automatically count for you once you set up your intervals.

11. Excel Histogram Generation STEP 1. Enter the basic data in either a row or column. STEP 2. Enter the RIGHT interval bounds in another row or column. STEP 3. Choose DATA ANALYSIS from the ANALYSIS group on the Ribbon data tab. Then select HISTOGRAM. Follow the instructions. STEP 4. Note that the PARETO box at the bottom of the dialog box should NOT be selected. PARETO is used in 6-Sigma analysis and Lean Manufacturing. It says basically that 80% of the errors come from 20% of the processes.

12. Excel Histogram Generation Note that the NUMBER OF INTERVALS is very important. Too FEW intervals, and there is a lack of detail and no information provided about the distribution. Too MANY intervals, and there are gaps within the distribution. A rule of thumb is to use 10-15 intervals. Fewer intervals might be better with a very small data set. If the data set is large (say n=900), then the square root of n provides a useful starting point.

13. Classwork and Homework Classwork is Problem 6.6 Homework is Problem 6.7

14. Cumulative Distribution Allows you determine whether some data value obtained randomly is less than or greater than some value. Sometimes cumulative distributions are expressed as a percentage instead of a decimal. The cumulative distribution is simply the sum of the previous relative frequencies and the current relative frequency. For example, in the 8 th interval, the cumulative distribution is the sum of the relative frequencies for intervals 1-8. The cumulative distribution last value is 1 (or 100%), never more, never less.

15. Cumulative Distribution in Excel Simply choose Cumulative Percentage in the HISTOGRAM Dialog Box. The graph of Cumulative Percentage will then be shown as a line superimposed upon the bar graph representing the histogram. Classwork: Problem 6.13 Homework: Problem 6.14