Transcript Xbar Chart Farrokh Alemi, Ph.D. Why Chart Data?  To discipline intuitions  To tell a story.

Xbar Chart
Farrokh Alemi, Ph.D.
Why Chart Data?
 To
discipline intuitions
 To tell a story
Steps to create an
X-bar chart?
1.
2.
3.
4.
5.
6.
7.
Check assumptions
Calculate grand average
Calculate standard deviation
Calculate standard deviation for each time
period
Calculate control limits
Plot chart
Interpret and distribute
Example Data
Over several
months, we
tracked the
satisfaction with
our unit.
 The question is
whether the unit
has improved
over time.

Time
Period
1
2
3
4
Ratings of Ratings of Ratings of Ratings of
1st
2nd
3rd
4th
Subject
Subject
Subject
Subject
80
84
82
80
70
72
74
70
76
78
76
78
80
78
78
80



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.
Satisfaction rating
Are variations due
to chance?
85
80
75
70
65
1
2
3
Time period
4
1. Check
Assumptions
 Continuous
Interval Scale
 Independent events
 Normal distribution
 Constant variance
2. Calculate Grand
Average
Average values for
all time periods and
all cases, plot as a
line
Satisfaction rating

85
80
Observed
75
Grand average
70
65
1
2
3
Time period
4
3. Calculate
standard deviation
Calculate standard deviation for all
observations
S = [i=1,…,nj j = 1, …m (Xij -GA )2 / (n-1)]0.5
GA is grand average
n is number of observations across time
periods
4. Calculate
standard deviation
for each time period
Estimate the standard deviation for each
time period
St = S / (nt)0.5
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
Calculations in
Excel
Grand
average
=Average(
B2:E2)
Constant
for 95%
confidence
limits
=Average
($B$2:$E$5)
Standard deviation
function over range of
all observations
Dividing by square root
of number of
observations in the
time period
Satisfaction rating
6. Plot Control Chart
85
80
Observed
75
UCL
LCL
70
65
1
2
3
Time period
4
7. Interpret findings
& distribute
First time period is
above UCL
 Second time period
below LCL
Satisfaction rating

85
80
Observed
75
UCL
LCL
70
65
1
2
3
Time period
4