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BOXCHART Statement 
The following notation is used in this section:
process mean (expected value of the population of measurements)  
process standard deviation (standard deviation of the population of measurements)  
mean of measurements in i^{ th} subgroup  
n_{i}  sample size of i^{ th} subgroup 
N  the number of subgroups 
x_{ij}  j^{ th} measurement in the i^{ th} subgroup, j = 1,2,3 ... , n_{i} 
x_{i(j)}  j^{ th} largest measurement
in the i^{ th} subgroup:

weighted average of subgroup means  
M_{i}  median of the measurements in the i^{ th} subgroup:

average of the subgroup medians:
 
median of the subgroup medians. Denote the
j^{ th} largest median by
M_{(j)} so that .  
e_{M}(n)  standard error of the median of n independent, normally distributed variables with unit standard deviation (the value of e_{M}(n) can be calculated with the STDMED function in a DATA step) 
Q_{p}(n)  100p^{ th} percentile (0<p<1) of the distribution of the median of n independent observations from a normal population with unit standard deviation 
z_{p}  100p^{ th} percentile of the standard normal distribution 
D_{p}(n)  100p^{ th} percentile of the distibution of the range of n independent observations from a normal population with unit standard deviation 
The skeletal style of the boxandwhisker plot shown in Figure 32.12 is the default. You can specify alternative styles with the BOXSTYLE= option; see Example 32.2 or the entry for the BOXSTYLE= option.
The CONTROLSTAT= option specifies whether control limits are computed for subgroup means (the default) or subgroup medians. The following tables provide the formulas for the limits:
Table 32.23: Control Limits and Central Line for Box ChartsCONTROLSTAT=MEAN  CONTROLSTAT=MEDIAN 
LCLX = lower limit  LCLM = lower limit 
Central Line  Central Line 
UCLX = upper limit  UCLM = upper limit 
CONTROLSTAT=MEAN  CONTROLSTAT=MEDIAN 
LCLX = lower limit  LCLM = lower limit 
Central Line  Central Line 
UCLX = upper limit  UCLM = upper limit 
In the preceding tables, replace with if you specify MEDCENTRAL=AVGMEAN in addition to CONTROLSTAT=MEDIAN. Likewise, replace with if you specify MEDCENTRAL=MEDMED in addition to CONTROLSTAT=MEDIAN. If standard values and are available for and , replace with and with in Table 32.23 and Table 32.24.
Note that the limits vary with n_{i}. The formulas for median limits assume that the data are normally distributed.
You can specify parameters for the limits as follows:
Note: You can suppress the display of the control limits with the NOLIMITS option. This is useful for creating standard sidebyside boxandwhisker plots (in this case, the STDDEVIATIONS option is also recommended).
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