Question 12.47

12.47 School absenteeism.

Here are data from an urban school district on the number of eighth-grade students with three or more unexcused absences from school during each month of a school year. Because the total number of eighth-graders changes a bit from month to month, these totals are also given for each month.

school

Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June
Students 911 947 939 942 918 920 931 925 902 883
Absent 291 349 364 335 301 322 344 324 303 344

639

  1. Find . Because the number of students varies from month to month, also find , the average per month.
  2. Make a chart using control limits based on students each month. Comment on control.
  3. The exact control limits are different each month because the number of students is different each month. This situation is common in using charts. What are the exact limits for October and June, the months with the largest and smallest ? Add these limits to your chart, using short lines spanning a single month. Do exact limits affect your conclusions?

12.47

(a) .
(b) . The process is in control.
(c) For October, .
For June, . Exact limits do not affect the conclusions.