Question

Budget lapsing at army hospitals.Accountants use the term budget lapsingto describe the situation that occurs when unspent funds do not carry over from one budgeting period to the next. Due to budget lapsing, U.S. army hospitals tend to stockpile pharmaceuticals and other supplies toward the end of the fiscal year, leading to a spike in expenditures. This phenomenon was investigated in the Journal of Management Accounting Research(Vol. 19, 2007). Data on expenses per full-timeequivalent employees for a sample of 1,751 army hospitalsyielded the following summary statistics: xbar= \(6,563,m= \)6,232, s= \(2,484, Q_L = \)5,309 and Q_U = \(7,216.

a.Interpret, practically, the measures of relative standing.

b.Compute the interquartile range, IQR, for the data.

c.What proportion of the 1,751 army hospitals have expenses between \)5,309 and $7,216?

Short answer

Answer:

1. The measures of relative standing are the quartiles
2. $1,907
3. 50%

Step-by-step solution

Interpreting the measures of relative standing

The first quartile is $5,309, implying that 25% of spending per full-time equivalent employee in army hospitals is $5,309. Spending on 75% of employees is less than $7,216 and more than $7,216 on 25% of employees.

The median indicates that spending on 50% of employees is more than $6,232, and spending on the other 50% is less than $6,232.

Computing the IQR

$\begin{array}{rcl}IQR& =& Q_U-Q_L\\ & =& 7,216-5,309\\ & =& \$1,907\end{array}$

Therefore, the interquartile range is $1,907.

Finding the proportion of expenses between $5,309 and $7,216

$5,309 is the lower quartile representing 25% of the expenses and $7,216 is the upper quartile representing 75% of the expenses. Therefore, 50% (75% - 25%) or ½ of the expenses lies between $5,309 and $7,216.