TOPICS

# Charlier's Check

A check which can be used to verify correct computations in a table of grouped classes. For example, consider the following table with specified class limits and frequencies . The class marks are then computed as well as the rescaled frequencies , which are given by

 (1)

where the class mark is taken as and the class interval is . The remaining quantities are then computed as follows.

 class limits 30-39 34.5 2 32 18 40-49 44.5 3 27 12 50-59 54.5 11 44 11 60-69 64.5 20 20 0 70-79 74.5 32 0 0 0 32 80-89 84.5 25 1 25 25 100 90-99 94.5 7 2 14 28 63 total 100 176 236

In order to compute the variance, note that

 (2) (3) (4)

so the variance of the original data is

 (5)

Charlier's check makes use of the additional column added to the right side of the table. By noting that the identity

 (6) (7)

connects columns five through seven, it can be checked that the computations have been done correctly. In the example above,

 (8)

so the computations pass Charlier's check.

Variance

## Explore with Wolfram|Alpha

More things to try:

## References

Kenney, J. F. and Keeping, E. S. "Charlier Check." §6.8 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 47-48, 81, 94-95, and 104, 1962.

Charlier's Check

## Cite this as:

Weisstein, Eric W. "Charlier's Check." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CharliersCheck.html