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Xbar Chart

Xbar Chart. Farrokh Alemi, Ph.D. Why Chart Data?. To discipline intuitions To tell a story. Steps to create an X-bar chart?. Check assumptions Calculate grand average Calculate standard deviation Calculate standard deviation for each time period Calculate control limits Plot chart

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Xbar Chart

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  1. Xbar Chart Farrokh Alemi, Ph.D.

  2. Why Chart Data? • To discipline intuitions • To tell a story

  3. Steps to create an X-bar chart? • Check assumptions • Calculate grand average • Calculate standard deviation • Calculate standard deviation for each time period • Calculate control limits • Plot chart • Interpret and distribute

  4. Example Data • Over several months, we tracked the satisfaction with our unit. • The question is whether the unit has improved over time.

  5. Are variations due to chance? • How would you answer this question? Look at the data. • There are wide variations in the data. Could these variations be due to chance? • The first step is to calculate the average for each time period.

  6. 1. Check Assumptions • Continuous Interval Scale • Independent events • Normal distribution • Constant variance

  7. 2. Calculate Grand Average • Average values for all time periods and all cases, plot as a line

  8. 3. Calculate standard deviation Calculate standard deviation for all observations S = [i=1,…,nj j = 1, …m (Xij-GA)2 / (n-1)]0.5GA is grand averagen is number of observations across time periods

  9. 4. Calculate standard deviation for each time period Estimate the standard deviation for each time period St = S / (nt)0.5

  10. 5. Calculate Control Limits UCL = GA + 1.96 * St LCL = GA – 1.96 * St • 1.96 sets the limits so that 95% data fall within the two limits • GA is the grand average • St is the standard deviation for the time period

  11. Constant for 95% confidence limits Grand average Standard deviation function over range of all observations =Average(B2:E2) =Average($B$2:$E$5) Dividing by square root of number of observations in the time period Calculations in Excel

  12. 6. Plot Control Chart

  13. 7. Interpret findings & distribute • First time period is above UCL • Second time period below LCL

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