4.3 Averages, Rates, and Unit Conversions
Key Takeaways
- An average is total divided by count; when a target average is given, multiply the average by the count to recover the required total.
- Rate questions compare two different units, such as records per hour, miles per gallon, pages per minute, or dollars per item.
- Unit conversions are safest when each step cancels one label and leaves the unit requested by the question.
- Time, money, distance, and measurement conversions should be written before calculation because wrong-unit answer choices often look plausible.
- An error log for this section should separate average setup errors, rate direction errors, conversion-factor errors, and rounding or unit-label mistakes.
Averages: Total, Count, Mean
The mean, or average, equals total divided by count. Civil service questions may give the separate values and ask for the average, or give a target average and ask what value is needed to reach it. In both cases, start with the relationship total = average x count.
Do not average averages unless the groups are the same size. If one office reports an average for 4 clerks and another reports an average for 12 clerks, the combined average must use totals and counts, not the two averages alone.
| Average task | Setup | Reasonable check |
|---|---|---|
| Find average | total divided by count | result falls between smallest and largest value |
| Find total from average | average x count | total is larger than one value |
| Find missing value | target total minus known values | missing value may be above or below current average |
| Combine groups | combined total divided by combined count | larger group has more influence |
Worked Example: Target Average
A call unit wants a 5-day average of 32 completed callbacks. That target requires 5 x 32 = 160 callbacks total. If the first four days total 121 callbacks, the unit needs 160 - 121 = 39 callbacks on the fifth day. The fifth day is higher than the target average because the earlier days were below target.
Rates: Compare Different Units
A rate compares unlike units. Common civil service rates include forms per hour, miles per gallon, dollars per copy, inspections per day, and minutes per file. The safest method is to convert to a unit rate first, then scale to the requested amount.
| Rate type | Unit rate question | Example label |
|---|---|---|
| Workload | How many per one hour? | files per hour |
| Time per task | How long for one item? | minutes per form |
| Cost rate | How much per one unit? | dollars per badge |
| Travel or fuel | How far per unit? | miles per gallon |
Worked Example: Work Rate
A records team indexes 189 files in 7 hours. The unit rate is 189 divided by 7 = 27 files per hour. At that rate, a 4-hour shift completes 27 x 4 = 108 files. If the question instead asked how long 108 files take, you would divide 108 by 27 to get 4 hours.
Unit Conversions
Conversions are label problems. Write the conversion factor so the old unit cancels and the requested unit remains. This habit is especially important when answer choices differ by a factor of 60, 100, 3, 12, or 7.
When a problem needs more than one conversion, handle one label at a time and write the intermediate unit. For example, inches can become feet before feet become yards. Skipping the middle step may feel faster, but it makes it harder to spot whether the final answer is in the requested unit.
| Conversion | Use it for | Common mistake |
|---|---|---|
| 1 hour = 60 minutes | durations and pacing | treating minutes like decimals |
| 1 dollar = 100 cents | fees and change | leaving cents as dollars |
| 1 week = 7 days | schedules and staffing cycles | using 5 workdays when calendar days are asked |
| 1 yard = 3 feet | simple measurements | multiplying when division is needed |
| 1 foot = 12 inches | room or storage dimensions | skipping one conversion step |
Worked Example: Time and Decimal Hours
A timer shows 2.4 hours. The whole number is 2 hours. The decimal part is 0.4 x 60 = 24 minutes, so 2.4 hours is 2 hours 24 minutes. It is not 2 hours 40 minutes, because the decimal is measured against 60 minutes, not 100 minutes.
Worked Example: Cost Conversion
A print vendor charges 9 cents per page. For 750 pages, the cost is 750 x 9 = 6,750 cents. Convert cents to dollars by dividing by 100, so the total is $67.50. The unit check is important because 6,750 dollars would be unrealistic for a small print order.
Error-Log Guidance
For averages, record whether you used the wrong count, forgot to recover the target total, or averaged averages. For rates, record whether you reversed the relationship, such as using hours per record when the question asks records per hour. For conversions, record the exact factor missed.
A strong prevention rule is specific: "When I see a decimal hour, multiply the decimal by 60" is better than "be careful with time." Review conversion misses in short drills before mixing them with full word problems.
A service desk handled 41, 36, 44, 39, and 50 tickets over five shifts. What was the average number of tickets per shift?
A clerk enters 135 records in 3 hours. At the same rate, how many records can the clerk enter in a 7-hour day?
A training video lasts 1.75 hours. How many minutes long is the video?