Moments


Mean	299.8524
Std Dev	0.0790105

Right click on the Moments in the Distribution output window. Select Make into Data Table. This should open up a new data table with two columns. The first column contains the names of the summary statistics and the second column contains the estimates. Double click on the Column 2 header. Rename the column Estimates and change the format to Fixed Decimal. Choose enough width (25 is sufficient for this problem) and enough decimal places (16 works here since the standard deviation has one leading zero and we want 15 places of accuracy).

	Estimates	Certified Value	l=-log₁₀[\|q-c\|/c]
Mean, m	299.8523999999999300	299.852400000000	l_m = 15
Std Dev, s	0.0790105478190506	0.0790105478190518	l_s = 13.8

Round the Mean Estimate to 15 significant digits (299.852400000000). You are now ready to compare to the certified values.

Mean, m: The Mean Estimate produced by JMP agrees with the Certified value to 15 significant digits. Therefore, l_m = 15.

Std Dev, s: The Std Dev Estimate produced by JMP disagrees with the Certified value in the last two significant digits. Using JMP to compute the lambda value, l_s = 13.8.

Minitab: Version 13

Stat – Basic Statistics – Display Descriptive Statistics

Descriptive Statistics: Speed

Variable N Mean Median TrMean StDev SE Mean

Speed 100 299.85 299.85 299.85 0.08 0.01

Variable Minimum Maximum Q1 Q3

Speed 299.62 300.07 299.80 299.90

Stat – Basic Statistics – Store Descriptive Statistics

Be sure to choose the standard deviation as well as the mean. Highlight the column that contains the mean and go to Editor – Format Column – Numeric. Select a Fixed Decimal with 12 digits. Change the column that contains the standard deviation to have a Fixed Decimal with 16 digits.

	Estimates	Certified Value	l=-log₁₀[\|q-c\|/c]
Mean, m	299.852400000000	299.852400000000	l_m = 15
Std Dev, s	0.0790105478190846	0.0790105478190518	l_s = 12.4

Mean, m: The Mean Estimate produced by Minitab agrees with the Certified value to 15 significant digits. Therefore, l_m = 15.

Std Dev, s: The Std Dev Estimate produced by Minitab disagrees with the Certified value in the last three significant digits. Using Minitab to compute the lambda value, l_s = 12.4.

Excel: Windows 2000

Enter the data into the first column. Insert functions for the AVERAGE and STDEV in appropriate cells. To get the correct number of digits use Format – Cells – Number and choose 12 decimal places for the mean and 16 decimal places for the standard deviation.

	Estimates	Certified Value	l=-log₁₀[\|q-c\|/c]
Mean, m	299.852400000000	299.852400000000	l_m = 15
Std Dev, s	0.0790105482336454	0.0790105478190518	l_s = 8.3

Mean, m: The Mean Estimate produced by Excel agrees with the Certified value to 15 significant digits. Therefore, l_m = 15.

Std Dev, s: The Std Dev Estimate produced by Excel disagrees with the Certified value starting with the eighth significant digit. Using Excel to compute the lambda value, l_s = 8.3.