MANAGEMENT MATH FOR MANAGERS R by Robert Miglino RRT, MPS
espiratory managers must use several applications of math: sta- tistical reporting, financial analysis, interpretation of performance
results, forecasting and cost analysis to name just a few. Usually there are two kinds of problems that crop up when it
comes to dealing with math as adults. The first has less to do with numbers as it does with decisions about which numbers to manipu- late, thus an ability to analyze and define a given problem becomes of paramount importance. The second problem has to do with either not remembering or not understanding math’s many formulas and rules. This is a problem for many of today’s generation of managers who were overwhelmed with formulas as students and under- whelmed with practical applications that could be visualized and grasped for better understanding. Let’s take a look at defining problems first. To define a problem
properly, one must be able to visualize it by gathering all the essential information concerning and affecting it. When that is done, the data and information has to be arranged logically so that it can be dealt with in order. Sequentially then, we can progress to a final result, conclusion, or number. Thus, when it comes to problems that require mathematical solutions, we must start with an analytical approach that visualizes the question before undertaking the solution. Example: Let’s say that an administrator calls you to discuss the
fact that nurses are having to draw more and more ABG’s at your in- stitution, significantly biting into their time. The administrator ac- knowledges that your department is already overworked, but still wishes to see R.C. perform all the inpatient ABG’s. He/She knows this will require more resources and so the administrator asks you to work on a report of what it would take to accomplish this goal. As director, you’re open to this idea but only if you can get the appro- priate increase in resources. You agree that this should start in the new fiscal year, one month away. After the analysis of all the factors that might come into play, you come up with the following facts.
1. The inpatient census is projected by M.I.S. to go up 6% next year. 2. Your own ABG logging system shows you that nurses are perform- ing 30% of the total ABG’s. 3. The materials manager tells you that you can expect a 10% in- crease in the price of ABG kits next year. 4. Materials management also states that reagents, controls, gases, supplies etc. will go up 8% next year. 5. You determine that you will not need another ABG machine. 6. You know and can later show that this will require hiring 4.2 more FTE’s for your dept. 7. You know from personnel that the entry level salary for new hires will be $30,000 plus 22% for benefits. 8. State lab agencies will raise their fee in direct proportion to the increase in actual samples analyzed. Your work has been in information gathering as you define what
will affect the proposal. Once you’ve ascertained your facts , the rest is just a matter of plugging in the numbers and performing simple math operations to arrive at numerical conclusions.
4 Focus Journal Fall 2011 The second reason so many people struggle with math is
that they never understood how the drills, theorems and arith- metic laws would ever apply to them. As a manager for instance, how often do you use square roots? Or compute pi? As a student however, you were expected to learn the calculations without practical applications. Here’s a rundown of some old favorites: FRACTIONS TO DECIMALS – To convert the fraction 2/7 to
its decimal equivalent, divide the numerator by the denominator. EXAMPLE: You want to requisition an extra part-time secretary to come in 2 days a week. That’s 2/5’s of a week, thus 2 divided by 5 = .4 of an FTE. FRACTIONS TO PERCENTS – To convert a fraction to a per-
centage, first convert to a decimal, then shift the decimal point 2 places to the right. EXAMPLE: You run an average of 12 vents per day. You own 7 and consistently rent 5. The hospital’s con- sidering buying more vents. In discussing this with your boss she asks you what % of vents running, are rentals. Answer: You know 5/12’s of your vents in use are rentals. Convert to a decimal by dividing 12 into 5. This equals .4166. Shift decimal point two places to the right = 42% PERCENTAGE INCREASE – Current factor –prior factor di-
vided by prior factor. EXAMPLE: In 2009 you did 32,000 Hand Held Neb Tx’s. In 2010 you did 37,000. What % increase does this represent? Answer: 37,000 - 32,000 = 5,000. 5,000 divided by 32,000 = .1562. Shift two places to the right = 15.6%. RATIO EXPRESSIONS – 3 main uses of ratios:
1. Percentage – i.e. occurrence of defects improved from 1 in 12 to 1 in 27 = 225% 2. X to Y i.e. 6,402 units compared with 5,812 = 1.1 to 1 3. Number of times – i.e. Improvement in cost per unit as in $1.96 to $1.44. All are calculated by dividing the later into the prior. ANNUALIZING – Multiply units by 12 then divide by num-
ber of months so far. EXAMPLE: It’s September 1st and you’ve done 336 PFT’s so far this year. How many are you on track to perform for the year? ANSWER = 336 x 12 = 4,032 divided by the eight months gone by so far = 504 for the year. INVENTORY TURNOVER – Cost of supplies used divided
by average inventory cost. EXAMPLE: In April you used $1,000 worth of nasal cannula’s which seems high to you. Looking over the previous three months you see that you used an average of $600 worth of cannulas per month. Dividing $1,000 by $600 = 1.66. You see that your inventory turnover rate was 1.66 times your previous 3 month average for April. GRAPHS – Graphs are visual representations of info. A
graph is meaningless without: 1. A descriptive title, 2. Footnotes, 3. Proper scaling. There are 3 basic graphs: 1. Line graphs used to demonstrate change over time. 2. Bar graphs, used to compare related info and relative significance, and 3. Pie chart graphs used to show relationships between information and each seg- ment’s contribution to the whole.
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